This is your summer to go abroad. The dollar buys far more in many countries than it did three years ago, which makes foreign travel one of the few things that is getting cheaper. Airline price wars have cut airfares down on some of the most popular tourist routes. Lower oil prices are keeping them down. If you wrote off foreign travel a few years ago as too expensive, take another look.

The State Department keeps track of what it costs a careful spender to stay in more than 800 cities around the world. By its count, Mexico City is 28 percent cheaper for Americans this year than it was in 1980. Paris is 22 percent cheaper; London, 17 percent cheaper. Athens--inexpensive to begin with--is down 11 percent. But Cologne is down only 3 percent, because of the strength of the West German mark.

Some cities are more expensive, like Rome--up 5 percent from 1980. The value of the Italian currency, the lira, has crashed, but Italian inflation keeps prices moving up. Tokyo--expensive to begin with--costs 17 percent more to visit than it did in 1980, because of the increased value of the yen.

In figuring costs, the State Department includes a hotel and three meals, all at moderate prices, plus 10 percent for incidentals. Here's what a budget traveler might expect to spend per day: Mexico City and Athens, $57 a day; Rome, $100; Paris, $105; Cologne, $108; London, $128 and Tokyo, $144. Travel agents say those figures are low, but they give you an idea of comparative costs. (For a free list of what traveling government employes pay, write to the Director of Allowances Staff, Room 501, State Annex No. 6, Department of State, Washington, D.C. 20520. Because government employes often get a discount, tourists can expect to pay 10 to 25 percent more in many cities than the list shows.)

Companies that package tours have also dropped their prices. American Express's Alpine special--two weeks in Germany, Austria and Switzerland--is down to $755 this year, from $970 in 1980 (not including airfare). Two weeks in Spain, Portugal and Morocco costs $910, down from $1,190 three years ago.

Asti Mexican tours offers seven days in a budget, beach-community hotel for $99 (not counting airfare), down from $124 in 1980. The same week in a deluxe hotel costs $179 this year. "If prices get any lower in Mexico, they'll be paying us to put people in their country," says Bronnie Coopers, president of Asti. She adds that the most expensive restaurant in Acapulco will cost about $16 per person.

Shortly after Mexico's most recent peso devaluation, some resort hotels continued to quote prices to Americans at the old dollar rate, which amounted to overcharging on a grand scale. But since then, the government has put price ceilings on hotel rooms.

In many countries, tourists can get more for their money by exchanging dollars at the black-market rate rather than the official rate. Should you do it? The standard advice has always been "no." Iron-curtain countries may arrest you if they find you dealing on the black market. Other countries may check your currency exchange slips at the airport, and detain or fine you if they look suspicious.

But a few countries make no attempt to curb such transactions. "We don't call it the black market; we call it the parallel rate, says Carlos dePaula at the Brazilian government tourist office in New York City. "You'll even see it quoted in government publications." Santo Domingo and Jamaica are two other countries where parallel rates are not illegal. In such places, tourists should check around to see who's offering what. Banks often give the low, official rate; money-exchange shops, hotels and shops may offer the parallel rate. Sometimes the parallel rate comes in the form of a discount if you pay in dollars rather than in local currency. If you pay with a credit card, you'll get the official rate.

Experienced travelers advise that you talk to other tourists, and to the big travel agencies in the country you're visiting, to see what the local practice is. Coopers says that the Mexican government takes a hard line against parallel rates.

Money-changing firms in the United States, like Deak-Perera, usually give the parallel rate if you want to exchange your dollars before you leave. But many countries restrict the amount of local currency you can arrive with--among them, Greece, Brazil, Italy and Portugal. So check the rules before exchanging money in advance.

In countries where you don't deal in parallel rates, your best exchange rate is usually at a local bank.