The nature of Soviet tourism and travel is that privilege didn't as express itself in terms of luxury as in Western tourism (bigger seats, better peanuts, etc.) but rather was defined by access to the various state-controlled agencies that handled tourism and travel. The Soviet elite had a much less restricted travel itinerary and far less hurdles navigating the travel bureaucracy.

The state subsidized both rail and air fare so much that prices often became divorced from cost, so in theory, any working-class Soviet stiff could afford to travel. In practice, tourism for the rank and file was an exercise in patience and "organizing" your travel plan. They typical early Soviet tourist though the Thaw had to navigate either through state agencies like Inturist, Sputnik (the Komsomol travel group), or various workplace-related tour groups. Air tickets in the 1970s typically had to be booked up to twenty days in advance and then one would receive confirmation up to two to three days before the flight.

You have to remember that on paper, the Soviet system was very egalitarian. Even the class distinctions between the elite and the bulk of Soviet travelers was not nearly as vast and sharp as what one would see in Western countries. Soviet elites might have higher quality hotels and food, but places like the so-called "Soviet Riviera" at Gagra in the Caucasus did not match the opulence of their Western analogues. However, where the Soviet system rankled many was its favoritism of its state apparatchik; in this case, they reaped more of the benefits of proletarian travel than those the system was to benefit.

Sources

Gorsuch, Anne E. All This Is Your World: Soviet Tourism at Home and Abroad After Stalin. Oxford: Oxford University Press, 2011.

Gorsuch, Anne E., and Diane P. Koenker. Turizm: The Russian and East European Tourist Under Capitalism and Socialism. Ithaca [u.a.]: Cornell University Press, 2006.