Mitchell's is my default bar. It's only a few blocks from my place, and it's got a great vibe. There's usually good music on the internet jukebox. The people are friendly, both customers and bartenders alike. The bathrooms here are atrocious (think jail toilets.. i've never been, but it's what I would liken them to). The drinks are cheap. Overall, it's a great little neighborhood bar.
A few notes :
-They do allow smoking. This seems odd to me.. spending the majority of my legal drinking years in Philadelphia bars, I'm not accustomed to being allowed to enjoy a cigarette inside. But bars in Pittsburgh seem more lax with this rule.. I dig.
-They don't take credit cards - this bar is cash only. There is an ATM directly across the street (PNC, I believe). It charges $2.
I saw something about being stared at for being the 'only white person' in the bar in a few reviews below.. I'm white, and I've never had so much as a sideways glance (because of my skin color, anyway). But if you're noticeably uncomfortable, I'd probably watch you too. Nothing like free entertainment.
EDIT - The women's bathroom has been remodeled.