Places I've been! (Warehouse District) W 6th St
D'Vine- It's a wine bar (but serves everything) with a "cafe-like" patio on the sidewalk. The inside is also fun. You can dress up or go casual. I went there last time I was in Cleveland and really liked it.
The Dive Bar- This is a bar at basement level. It gets pretty packed with younger people and is the meeting place of the Young Buckeyes (OSU Alumni in Cleveland) It has Buckeye Football stuff everywhere. I went here for a bachelorette party and had sooooo much fun.
Panini's- Very relaxed, casual serves food. Mainly a beer, sports bar-type establishment. They serve sandwiches with fries on them! There is also a Panini's in Coventry
The Velvet Dog- Club scene w/ dance music (not techno), 3-levels and a roof top bar. Kinda fun if you're with a group, but there is the occasional creepy, too drunk (or drugged) guy you just want to run from
Also, has booths with curtains so that you can't see what the people are doing in them. I would not suggest sitting there!
OK- So these are the places I've been in Cleveland. D'vine and The Dive Bar are my favorites. I hope this is helpful!