This is the logo for a store in Boston called Acquire. Does anyone know what the typeface is?

Whatever it is, the Q was most probably customised.
The sample is pretty small, here are a couple of similar ones:
http://www.myfonts.com/fonts/bitstream/imperial/
http://www.myfonts.com/fonts/paratype/newton/
http://www.myfonts.com/fonts/adobe/gazette/
http://www.myfonts.com/fonts/paratype/academy/

Most probably Cochin, simply needs to pull upward the /Q's tail.