We stayed for 4 nights at the RT Regent. The staff were very helpful and friendly and arranged trips and taxis for us. The room was very clean and comfortable and for the most part quiet.
It is ideally situated right in the heart of Kazimierz, a few
minutes walk from Plac Nowy and the surrounding bars. If you're aiming at avoiding tourists the majority of the bars here are filled up with locals (though if your Polish isn't up to scratch most of the barmen understand enough English to get by).
On the second night we were there a large group of kids arrived (we never managed to work out their nationality), who proceeded to run about causing mayhem for much of the night (there was a lot of crashing about and things being knocked over) but they were gone after that.
I would recommend staying here!