Size (largest to smallest): Kiev, Krakow, L'viv
Off the path(most visited to least ): Krakow, Kiev, L'viv
Lodging (expensive to cheapest): Kiev, Krakow, L'viv But they are all sub-€100/night.
Food (expensive to cheapest): Kiev, Krakow, L'viv
Nightlife (best to worst): Kiev, Krakow, L'viv

All three are university towns with large student populations if you are in that age range.
You haven't mentioned how you are planning on getting to the place of your choice. Roads in Ukraine are horrible and the trains take forever. Krakow can be reached by trains from Warsaw, Vienna and Prague, not to mention by bus from most large European cities. All 3 of your potential locations are served by low-cost airlines too.