It's true...Chelsea and Greenwich Village have a fuck ton of gay bars. Stonewall is the most famous one but there are many others too. But going back to non-gay bars...my favorite non-gay bar downtown is the Holiday Cocktail Lounge in the East Village. Their drinks are fairly priced (cheaper than Bull McCabe's and many other bars) and unlike Continental (another cheap ass bar in the area that prides itself on offering 5 watered-down 1 oz shots for $10), the drinks are actually good quality.
I'm still on meds now so if I go to any bars, I probably won't drink anything other than water. I'm hoping to change that eventually--just not sure when. It'll probably take years. AEDs are a fucking bitch.