Restaurants: Go to either (or both of) Torrisi and Parm. They're right next door to each other on Mulberry just south of Prince. Torrisi is a bit more of a fine dining spot, they do a different 7 course prix fixe menu every night (they also have a lunch seating) while Parm is a bit of a throwback soda shoppe type place specializing in italian but with a few twists (the meatball parm sandwich is amazing and the calamari is the best I've ever had. I can't even talk about the mozzarella sticks without tearing up a little). If you go with Torrisi you'll want to call now to see if they have an opening as it fills up every single night, Parm is walk in only but you can put your name down and then wander around the area for a while.
There are tons of great restaurants, a good source is the New York page on eater.com. They have these "restaurant heat maps" of all of the places that are considered the go to spots at the moment.
Concerts: There are always a ton of shows in NYC, and it seems like there are more than usual right now. Just did a quick search on Pollstar and some notable (to me at least) shows include Active Child (with Band of Skulls who are great live) and M83. There are tons more, and pollstar isn't always inclusive, but here's the link
http://www.pollstar.com/resultsCity....new+york%2c+ny
Broadway: I haven't been to Phantom, but I don't think it's that hard to get. I had friends come into town a couple years ago and get tickets pretty easily. Book of Mormon is obviously the hottest show in town right now, and everyone I know who has been has loved it. I saw How to Succeed in Business Without Really Trying recently and enjoyed it, but it was a little slow.
You can get discounted same day tickets at the TKTS booth in Times Sq (I've heard there's one in Brooklyn too, with way shorter lines) but you're sort of at the mercy of what comes available that night.
Sporting Events: Yankees games are a good time, and it's typically pretty easy to get cheap tickets in May, especially for weekday games. It's an easy trip, just take the 4 train to the Yankee Stadium stop. There are three good pre/post game bars up there, Billy's and Stan's (I think it's Stan's) and the Yankee Tavern. Billy's is the biggest, nad after weekend games part of it turns into the weirdest Staten Island/Jersey Shore dance party. It's the best people watching I've ever done.
Rangers and Knicks playoff tickets will be steep, especially later in a series. Tickets for last nights game 7 were going for $300 minimum, for game 7 of the second round I'd expect you'd be looking at $500 for 400 level seats. Knicks tickets are always steep, and if they've pushed the Heat to 6 I'd expect they'll be in the same range.
The Devils will also be hosting game 6 (assuming it gets that far) while you're in town. Devils tickets are much easier to come by and The Pru Center is literally 15 minutes from MSG and incredibly easy to get to.