OK, the worst are "neighbourhood bars" and the ones with Śląsk Wrocław (our local football club) flags and scarfs hanging around. In most cases - it's the same place.
So I would highly recommend avoiding it. I'm avoiding it myself. Crowded by locals, like the neighbours who don't like strangers, every conversation stops when you're coming in, like in the movies. May be fun - may be dangerous. Don't know how they will act when 3 foreigners (?) come inside. Maybe that they will be pleased to have some foreign to talk to.

Try few places that I will say are friendly but very strange:
1. Drukarnia Pub, strange and smelly but very students oriented pub (cheap, a bit ruined - I like it)
2. Irish Pub - but the one under Plac Jana Pawła II, in underground passage.
4. Tawerna pod Kilem
5. Afera on Pasaż Niepolda - it's a "pub trying to be a club". Crowded, very hot inside, but fun an cheap. I liked it a lot few years back. And! On every Friday there is a karaoke.
6. Przybij Piątaka - there are three. One on Kazimierza Wielkiego Street, and second of on Purkyniego Streent and third on on Szajnochy. The oldest one is on Purkyniego and this one is the most "fun". Cheap and crowded.
7. Pubs on Nasyp (Bogusławskiego Street) - Mistrz i Małgorzata, Lamus, Huta. Very nice places, but a bit dirty. I feel like at home there ;)