Pittsburgh is wonderful. There's a lot wrong with it, but a lot of right too. It is certainly very cheap to live, and there's a lot going on. We even have a Techstars-affiliated incubator, which used to offer a really, really good deal. My first startup, CloudFab, went through it years ago. That said, SF is still the best place in the world to do a startup: every city says "We may not be SF, but we have X!" X is _never_ enough to make up for not being SF. I said it when I lived there too, and now that I've lived in SF, I know that's just deeply, deeply wrong. That doesn't mean you _can't_ do it, but it's a handicap.
However, living in a place is very rarely about 'economic sense.' I have a _need_ to live in NYC. I've gotten more work done in the two weeks I've lived here than I did in the entire six months I lived in SF, and maybe about a third of what I did in LA. The hustle, bustle, and opportunities are endless.
Last night I woke up at ten am, did my laundry, then went to a juice bar, worked for a few hours, walked around, ended up literally coding on a bar while watching the US. vs. Ghana game, then took the train over to Herald Square and coded in the park. It was a beautiful evening. Around midnight, walked up to Times Square to squeak in some power before all the stores closed, then worked in another park until 3am, and took the train home. You can't really do that anywhere else, at least in the states.
Oh, and I'm saving about 25% on my rent by moving to Brooklyn from San Francisco, and I'd be saving 60% if I had still lived in the Mission when I left.