No offence to our Polish friends from Lodz but it isn't one of Poland's gems. Katowice, an hour from Krakow, 2/3 hours from Wroclaw and (for the religious)1/2 hrs Czestochowa, is a much better base and somewhat nicer city. And you're near the mountains. Actually only an hour to the Czech city of Ostrava.
Mind you I'd still prefer to be in Krakow as it is really is a wonderful city to stroll around day or evening.
But why base yourself in any one city ?
Why not use the extensive and cheap train and bus network and do a tour on your own.
You could start at Lodz grab the bus to Wroclaw, then Krakow area with side trip to mountains and Ostrava.
It depends on your time there I suppose and whether you don't mind changing hotels.