With all due respect to Steve, I would suggest avoiding the more Touristy parts of NYC, if you do go to Steve Maxwells you will see Times Square, but I wouldn't waste time there, It's not real New York.
If you move to the East and West you'll see the more everyday city, were residents eat and live, The subway system is a very efficient way to travel, and is air conditioned, which you really need right now!
Time Out New York, link here:
is a good source of information about live music.
The Guitar Center on 14th street is pretty good, a decent drum section, and helpful staff, have you considered, as you'll have a residential address during your stay, buying from places like Amazon?