It was 8 p.m. on a recent summer's night and Lajos Boross tucked his violin beneath his chin and once again began to make the rounds of the tables at the Margit Garden Restaurant. But instead of playing one of those haunting Gypsy melodies or a tune from a Lehar operetta - as would be expected here in the heart and soul of Hungary - he broke into a touching rendition of "Sophisticated Lady."

Welcome to Budapest, the city of pleasant surprises, where the visitor can find gypsy violinists playing Duke Ellington, splendid three-course dinners with wine for less than $10 and a capital city that is among the most beautiful in all of Europe, a city that has been rebuilt in its own Old World image after literally being demolished by war.One thing that won't surprise visitors is that Budapest is named after its two main parts - Buda and Pest.

Sitting like rival sisters on opposite sides of the Danube River, both Buda and Pest wear an ornate architectural fabric of subtle-colored finery, yet each is distinct in direction and demeanor while being stitched inexorably together by a network of bridges that nurtures them with a constant flow of city life.

The first span to link the flat plains of Pest on the Danube's left bank with the rolling hills of Buda on the right was the Chain Bridge, an engineering and scenic marvel of its time when it opened to traffic in 1849.

Tragically, the historic neo-classical structure and the other Danube bridges were destroyed during World War II, which also saw three out of every four buildings in the city laid to waste.

As they had done in other centuries after other battles, the residents erased the scars of war by painstakingly rebuilding their devastated treasures in their original form.

A visitor today, walking across the Chain Bridge, or strolling through the former Royal Palace (now the Historical Museum), or attending a performance at the State Opera House, restored to its former grandeur, would be hard-pressed to tell that most of the city had been reduced to rubble just a bit more than four decades ago.

In rebuilding the past as a monument to their future, the tradition-minded and fiercely prideful Hungarians also created a booming tourist industry that attracts visitors equally from Eastern bloc countries and the nations of the West.

In fact, Hungary, which is about half the size of Missouri and has a population of 10,600,000 (one-fifth of whom live in Budapest) welcomed almost 19 million foreign visitors last year and that number is easily expected to be surpassed this year.

And judging from the number of Germans, Italians, Scandinavians and Americans seen, Budapest's tourism charms have also succeeded in "The Winning of the West," from where, so far this year, there has been an astonishing 50 percent increase in visitors over 1987.

The culture shock here for a U.S. visitor is that there is no shock as far as Hungary being a Communist-controlled country is concerned. If Big Brother was watching, we couldn't find him. While some 65,000 Soviet troops are said to be stationed in an around the city, they were not to be seen during our visit.

Budapest is one of the best value destinations in the world, with prices as much as 70 percent less than New York, Paris, London and Rome. A 15-mile, 45-minute taxi ride from the airport to the hotel, for example, costs $5 with tip. A ride on the public transit system is less than 5 cents. A three-course meal with wine in a local restaurant is $7 with tip.

While rates at the newer hotels are high compared to other prices - approximately $130 a day double - they are still less than in most of the Western capitals. We stayed at the four-star Forum Hotel on the banks of the Danube in Pest. Considering the superior service and accommodations, we're still trying to figure out why the Forum doesn't rate five stars.

After this fall, more U.S. tourists than ever can be expected in Hungary, because some 7,000 members of the American Society of Travel Agents will hold their convention here from Oct. 24-28.

For information on travel in Hungary, contact Dr. Miklof Walko, director, Ibusz Hungarian Travel Co., Suite 2455, 630 Fifth Ave., New York, N.Y. 10111.