Beer Bar Near Chinatown/Reading Market?
There's actually a beer garden in the RTM, with 24 taps: http://www.mollymalloysphilly.com/. There's also the new-ish BarLy in Chinatown, I haven't been there yet but they have 60 taps: http://www.bar-ly.com/menus/. If you head a few blocks south of there, Time and Smokin' Betty's both have good beer lists. If you're looking for a particular beer, you can try finding a place that serves it at http://phillytapfinder.com/.
I would also consider Bru at 1318 Chestnut. Its an indoor german style biergarden with a good beer selection.
With regard to Molly's in RTM, while it has a lot of taps, I find it highly unlikely you are going to find beers there you are not going to find at better places in Manhattan especially if you go to places like the Gingerman or Dbs.
Not too far a walk would be Monks. One of the best Belgian beer selections on the East Coast though you would have to cross Broad street.