... and the good news is that at the end of June you'll be able to watch the Mets beat the Yankees at Yankee stadium! But seriously, if you like baseball it would probably be cool to hit both Shea and Yankee Stadium since they are both in their final seasons.
A few places that I used to frequent:
bar: Art Bar on 8th Ave (between Horatio and Jane)
lounge: Stone Rose, Columbus Circle
best Chinese food in the city: New Green Bo, 66 Bayard St
best Thai: Peep on Prince St (few blocks west of the SoHo Apple Store)
Also, an interesting museum that most people don't get to and that is especially beautiful in the summer is
The Cloisters. It is way uptown but if the website draws your interest I can assure you it doesn't do it justice.
I'm also fond of spending time in Central Park, catching a play off-broadway and believe it or not, even as someone who lived there for years, those double-decker bus tours that leave from Times Square can be pretty fun.
And as far as the Apple Stores go, go see 5th Ave if you haven't before, but it's just an annoying, overcrowded tourist trap.