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.

GREECE:

For this tiny Mediterranean nation of 9 million, the biggest hassle this summer will be the sheer weight of numbers, with 5.5 million tourists anticipated this year.

Therefore, stay away from the more popular, developed resort areas and seek out the less "in" places, such as the islands of Karpathos, Kalymnos, Patmos and Alonysos, plus any in the southern Cycladic chain. All are accessible by boat from the Athenian port of Piraeus.

If you're truly interested in avantgarde living, don't book rooms in advance. Linger in the island port on arrival and you will inevitably be found by a score of young boys and grandmothers, all with rooms to rent.

Almost without exception, you will be ushered into an immaculate, white-washed home, complete with tiny courtyard for breakfast, under the shade of an orange or lemon tree. This is the best way to see and feel the country. Your dollar will go far on the islands, where life has remained remarkably simple and cheap.

If you're not keen for such an adventure, but want something a bit more imaginative than a standard hotel, the National Tourist Organization has embarked on an ambitious program of renovating large, abandoned homes in the countryside, turning them into tourist retreats. Such pensions now operate in Oia Santorinis on Santorini Island, in Fiskardo on the island of Cephalonia, and in Makrynitsa and Vizitsa in mountainous Pylion.

Athens, a sprawling mass of concrete and asphalt, should be avoided: Only the classical sites remain to be seen. Overnight and see the Acropolis, perhaps your last chance to observe the edifice in its natural state. Pollution has so ravaged its marble that plans are now under way to remove the original sculpture at an unspecified future date.

Make a sidetrip to the Agora, the marketplace of Periclean Athens, and the Roman market nearby, then down into the Monastiraki - the city's flea market - with its cluster of tiny, hole-in-the-wall shops. Buy handicrafts, bronze and copper, sandles and leather goods.

Finish the afternoon, whether you are in Athens or anyplace in Greece, by sipping coffee in an open-air cafeneion. Greeks are inveterate "people watchers" and sitting with them, doing nothing, is part of the local scene.

Thankfully, custom dies slowly in this country and life outside Athens evolves at a relaxed, casual pace. Take a nap between 2 and 5 when everything closes for the siesta. Do not plan on having dinner until 9. Bring lightweight, casual clothing, though on the islands a sweater is often needed at night.