Budapest — The gray-haired woman from East Germany attending a performance of ''Aida'' by the Hungarian State Opera in Erkel Theater was not one of those regarded as a ''profitable'' tourist by officials here. Aside from room and board, the German Democratic Republic allowed her about $7 worth of Hungarian forints for spending money during a four-day stay.
''Es macht nichts'' (''It doesn't matter''), she said. And since her excellent seat at the opera cost only $1.11, and a subway ride some 5 cents, her money would go further than one might expect.
From the Hungarian government's standpoint, the German woman not only had little money to spend, but it was exchanged from a nonconvertible currency. ''Profitable'' or ''good quality'' tourists come from noncommunist countries with hard currencies.
Over the past few years, Hungary has seen a sharp decline in the number of visitors from Eastern Europe because of the Polish crisis and travel restrictions by Czechoslovakia and Yugoslavia. But there has been a good increase in those arriving from the noncommunist nations. And that's better than vice versa, figures Istvan Meggyes, deputy general director of the Hungarian Tourism Board.
(Tourist arrivals from the United States were up 17 percent last year, to 70, 000, and could reach 100,000 this year, according to a tourist official in New York.)
Last year, Mr. Meggyes noted, hard-currency visitors spent $260 million in Hungary, of which $160 million was net dollar profits after deducting hard-currency expenses for these tourists. They come to see the abundant museums , enjoy the inexpensive cultural festivals, use the various spas, or visit the countryside.
Hungary regards tourism as important because it is a relatively easy way to earn foreign exchange that can be used to buy desirable technology and tools in the West. And since the nation has a brand of communism that is relatively relaxed compared with, say, Czechoslovakia or Romania, the government has less fear of ideological contamination.
In fact, during the last few years it has been driving to construct hotels that meet, as Mr. Meggyes put it, ''international standards.'' With the help of a $300 million credit from Austria that financed the use of Austrian contractors , Hungary has built four modern hotels. Room capacity jumped 40 percent in 1982.
''Hungary has always been famed for its traditional hospitality,'' Meggyes said. ''Now we can meet Western-style economic efficiency in our hotels.'' These hotels are licensed and inspected by such chains as Hyatt, Forum, and Penta, and , in the case of the Hilton, managed under contract.
Altogether, Hungary had 6.8 million tourists last year, up about 300,000 from 1982.
Tourism remains underdeveloped when compared with that of, for instance, Austria next door. But this is recognized by the tourist authorities, and they have plans for encouraging more tourists. These include:
* Scheduling various events, such as a gastronomic festival, an exhibition of fine arts, or a spring arts festival, before or after the summer tourist season, when the hotels are jammed. Year-round occupancy of the better hotels runs 63 to 65 percent.
* Increasing and improving the number of tourist rooms.
At the moment, the Austrians are reconstructing some of Hungary's older hotels to bring them up to snuff. The tourist office is also trying to stimulate an increase in the number of private pensions, camping sites, rooms available in private homes, and rural tourist facilities.
* Encouraging both private entrepreneurs and employees of state-owned hotels to improve services for tourists.
For example, the state will now lease a restaurant it owns to a manager for, say, five years at a specific rent. The manager is able to hire up to 12 employees and run the restaurant for profit.
''The idea is to make them interested in better service . . . for the clientele,'' said Mr. Meggyes.
At the larger hotels, managers and employees reap special bonuses if the hotels make better profits.
* Opening next February a convention center in Budapest with meeting facilities for up to 2,000 in one hall. A modern new airport next to the inadequate old one is also supposed to be finished next year.