THOUGH SOME industry officials are hedging their bets, many travel pundits predict that Americans will play tourist abroad in record numbers this season, despite the poor showing of the dollar and continuing inflation. Europe remains a major destination, with bargain air fares providing an important incentive.

What conditions will the traveler find in some of the most popular European countries? What tips will help make the dollar go further? Following are brief reports from writers in three capitals. ITALY:

The best advice for anyone planning to visit Italy this summer is to come armed with a good supply of patience. The situation changes from day to day, but there's a good chance of running into wildcat transport strikes by pilots or other airline personnel on the one hand and by railroad workers on the other.

Recently, for example, the so-called autonomous railway workers - that is, those who do not belong to the giant Triple Trade Union Confederation, have staged eight days of on-again, off-again strikes that have most of the trains here running between one and two hours behind schedule. As for air travel, forget it. If its not the pilots, it's old-fashioned Italian airport inefficency.

As for inner-city transportation in Rome, the buses at 100 lire (about 11 1/2 cents) are a bargain if you're not traveling during rush hour. Taxis, too, are cheaper than in most American cities, but one word of warning. You're likely to be taken for a ride by your cabbie, so read the foreign-language rate schedule posted near the door and stick to your guns.

At present, rides to and from the airport get an additional 4,800 lire (about $5.50) above the meter. If you call a cab, you pay an extra 100 lire. There is a 350-lire supplement for evenings after 10, and for Sundays and holidays, but anything more is part of a Roman cabbie's all-too-frequent attempts to make an extra buck - at your expense.

Italy's a fairly good buy this summer but there are two ways to make your dollars go further. One is to eat only one of your two daily meals in a restaurant, while going to "tavola calda" or even a carry-out pizza place for the other. By the way, any grocery store (look for Salumeria, Drogheria or Alimentari on the storefront) will be glad to make you up a sandwich and sell you wine, beer or even a Coke for a do-it-yourself carry-out lunch.

The other word of advice, is "hold on to your purse." Don't hang it on your chair at an outside restaurant or cafe, and while strolling keep your purse to the wall side and your ears peeled for approaching motorcycles (driven by hoodlums who've raised purse-snatching on the run to an art).

If you've only time for one proper meal here, the best thing is to have it out of doors on one of those marvelous Roman summer nights. I recommend either "II Bolognese" in Piazza del Popolo if you like to eat well and watch the beautiful people, too, or "Gino" in Trastevere if you're mad about fish. Don't forget that even though service is included you should still leave a tip of several hundred lire extra per person.

There really isn't much going on in Rome during the summer, so what most Romans do is to finish off the evening with ice cream or a drink at one of the cafes in Piazza Navona. It's crowded and noisy, but it's really Rome.

NEXT SUNDAY: Paris, Germany and Switzerland.