Sounds like Warsaw suits your purpose. Good for business, good for nightlife, and everywhere else you might want to go is convenient by plane, car, or rail.
Start there and move later if you fall in love with the mountains...which you probably will.
I paid 68 to 89 usd in Krakow and Lodz for the end of March. Nice hotels at the city centres. KasiaG is right, I saw some nice B&B's in Krakow that were very reasonable..and apartments as well. poland.com and staypoland.com both have pretty good listings of what's available.