1982... your game is almost over.
If you're close to domination or conquest victory, then do what you have to, in order to win. e.g., if you need only 5% more territory, then keep all the cities (burn none). You also may want to pay cash for a few temples or something so that your cultural borders expand in those new cities.
If you're close to conquest, then you probably want to burn them all. Any city, even quite tasty ones, will slow down your military machine for a few critical turns, and lower your economics so you can't pump out as many tanks or whatever.
Otherwise, if you're high score and nobody's close, then all you really need to do is get to 2050 AD and you'll win. So, keep tasty cities and burn the rest. Don't waste your time, though, trying to manage a lot of conquests. It won't affect the outcome so why bother.
Also, look at the Info screen to see which ones have wonders. Keep those.
Wodan