Must Europe's major cities be declared out-of-bounds to the go-it-alone American traveler of less than affluent means? Should we independents scratch such European destinations as London, Paris, Rome and Vienna from future foreign itineraries?

Not if we still have Yankee ingenuity and a spirit of adventure.

We all know what has happened to the purchasing power of our money. The combination of inflation and erosion of the dollar's value against foreign currencies has pushed the cost of such basics as bed, board and transportation to a point where one is likely to think carefully before making plans for a European trip that includes stays in one or more capitals.

There are horror stories about $150-a-day hotel rooms in London, a meal for two in Paris for $100 or more, the $20 Roman taxi ride, a cup of coffee and piece of cake that can cost $8 in a German city. And the tales turn out to be true.

One need not be a mathematician to figure out why this should be so. In addition to an unfavorable exchange rate there are spiraling costs of goods and services, along with the law of supply and demand. In the case of big-time hotels abroad, prices are geared to a clientele of expense-account businessmen, visitors from the oil-rich Middle East and South America, along with Japanese who have the yen to travel.

On the plus side, in recent weeks the dollar has bounced back remarkably in Europe -- particularly against the German mark and French franc -- and reached its highest level in years. Still, even with these perhaps temporary breaks, how to cope with a set of fairly tough conditions remains a major concern for anyone planning to visit Europe in the high season ahead.

European tourist offices frequently advise Americans they will spend less money on a European vacation if they skip the big cities and concentrate on the charming countryside instead.

Rather than stay in London, put up in a romantic country inn in the Cotswolds, officials say. Pass Paris by for rural Normandy. Settle in a converted villa among Tuscany hills at a fraction of the cost of staying in Rome's Excelsior. Trade Munich for a family-run pension in the Bavarian Alps.

All of which is fine for those who like it that way. But there are others for whom the lure of Europe is primarily within the big cities. We don't cross the Atlantic to settle for second best.

The excitement and splendor of Venice cannot be equated with some rustic backwater, no matter how admirably it may be situated. Paris is the pay-off, and no substitute will do. Amsterdam, Brussels, Copenhagen . . . these are magic names, along with Dublin, Edinburgh, Lisbon, Madrid. And for some of us the ideal way to experience any of these cities is still on our own, not locked into a package tour program (though for the first-time visitor on a budget, today's tours offer tempting prices and more flexibility than in the past).

How to achieve this under current circumstances without going broke in the process requires a certain ingenuity and imagination, but it can be done.

Cost-cutting is the name of the new game -- doing without, and doing things differently than in the past. Pinching our pennies. Improvising to some extent. Making fewer demands in terms of comfort and convenience. Reassessing our priorities. Finding that we can get by with less of everything and still survive.

In fact, there is a built-in "plus" factor involved in coming to terms with the new reality of Europe's cities. Less can indeed add up to more. Travelers are forces to become involved in the life of a place in a way that was hardly necessary in the pampered days when the dollar bought considerably more abroad than at home -- which is exactly what travel was all about in the good old days of a decade or more ago.

Then one could stay in the most expensive hotels, eat in the finest restaurants, depend on taxis to get from one place to another. All one had to do was phone a friendly travel agent and say, "Hey, set me up for a week or 10 days in my favorite European city." No more. And the very challenge of being forced to do it on our own and on our own feet can make for an extra-special experience.

But to beat the current system requires pre-planning and doing some homework. The major factor aside from air fare in trying to control the cost of a European stay is to locate accommodations and food at a budget price one can live with. This means that from Amsterdam to Zagreb we will have to forget about staying at the Hilton or Inter-Continental.

Unfortunately, travel agents are often of minimal help in locating the smaller, low-priced European hotels, and the reasons are more complex than the somewhat deprecating statement, "the higher the price of the room, the bigger the agent's commission." In fairness, competent, professional travel agents do not prosper by giving poor advice based on greed, though they work on a low margin of profit and time is money. Even a good agent cannot be expected to personally know of many of the small inns abroad (some of which do not pay commissions). Additionally, the U.S. tourist is competing with knowledgeable European travelers for the small number of rooms at these bargain prices.

The lack of fast, computerized reservations systems such as those serving big hotels means the agent must phone, cable or write -- costs that may be legitimately passed on to the client. Small inns often do not reply if they have no room (return postage must be sent if an answer is expected). Booking must be done far in advance -- yet Americans are now making vacation plans later and later. And, finally, "small" does not always mean "cheap," since some of the finest inns have rates that would break a low budget.

The answer is to do it yourself. Friends of this writer who could easily afford to go in grand style but prefer to do otherwise have devised an ingenious method for finding serviceable small hotels in advantageous locations in European cities. Working with city maps, guidebooks (such as the Michelin Red Guide, Fodor, and the Arthur Frommer Dollar Wise series), they first locate some of the biggest and most expensive hotels in the city of their choice. Then they track down much smaller and less expensive hotels in the immediate vicinity.

In the case of Paris, they would zero in on the area around Place Verdome, site of the Ritz, Meurice, Lotti and Inter-Continental, where a double room can easily cost $150. But practically next door to the prestigious Meurice is the 66-room Brighton, where prices at last check started at under $50 for two. The Family Hotel, in Rue Cambon, directly behind the Ritz, has 23 rooms, all at under $50. And there are at least three other hotels in the area -- all listed in the Michelin Red Guide -- that qualify as good values.

The next step is to write letters to each of the hotels under consideration, specifying dates, length of stay and so on. In the event that all hotels offer suitable accommodations, choose the one with the greatest appeal, send a personal check for the amount of the deposit specified, and as a courtesy, inform the other hotels that plans have changed.

It is also a good idea when making an inquiry -- particularly in the case of very reasonable hotels -- to enclose two International Postal Reply Coupons available at any post office for 42 cents each, to cover the cost of return mail. An air mail letter from Europe invariably comes to the equivalent of 75 cents or more. Usually the check sent as deposit will be returned to the sender on arrival. Payment for your vacation may have to be in cash. Remember: Credit cards are not always accepted in small, independently-owned hotels abroad.

This system can certainly be worked to advantage in France, Italy, Switzerland, Spain and West Germany. Of course, there are numerous other excellent small hotels in Paris not located near grand-luxe establishments, as on Ile St. Louis. And in Venice inexpensive hotels line Lista di Spagna, just off from the railroad station turning to the left from the exit. Athens and Lisbon still offer some of the best hotel deals in the world. Surprisingly, for high-priced Germany, Munich has some hotels that could be considered in the budget category. That's also true in Bamberg and Nuremberg.

London and Vienna have acquired the reputations of being very short on low-priced lodgings. But there are now 2,000 inexpensive rooms in central London, according to the British Tourist Authority (BTA). Sussex Gardens apartments, just north of Hyde Park, offer about 1,000 rooms, with a single costing $24 a night and a double $35, both without bath. Similar rates (within a few dollars and also guaranteed through Oct. 31) for an additional 1,000 rooms are available in Kensington and Chelsea. For brochures on these, write to BTA, 680 5th Ave., New York, N.Y. 10019. It is also possible to find reasonable accommodations in the suburbs, reached via tube or bus -- and, of course, there are always B&Bs (Bed and Breakfasts).

It is more difficult in Vienna. One solution there is to overnight in the spa of Baden (15 miles to the south) and commute daily into the city by tram, bus or train, saving roughly 25 percent over rates in the capital.

The Arthur Frommer Dollar Wise guides probably offer the most complete and up-to-date listing of satisfactory hotels in a budget category.