That's awesome, of your 4 destinations, I've been to NY, LA and San Antonio.
Some tips
LA: make sure your accommodation is close to where you want to be (for example West Hollywood is not that close to Hollywood, i learnt the hard way), getting around in LA is a pain buses are terrible, and cabs are hard to find be prepared to do a lot of walking.
NY: Although you'll pay a lot for it, I suggest try staying close to Times Square, its central to everything, NY subway is awesome to get around trains every 5 minutes. The Flagship NBA store may be open by then so defiantly check that out (apparently its going to be near Madison Square Garden), I missed the closure of the old store by about 2 weeks. Don't pay for a Statue of Liberty tour, just jump on the Staten Island ferry which is free, it goes right past the Statue of Liberty anyway. My favorite bar in NY is called "The Australian" only about 5 blocks form Time Square, great place for an Aussie burger or Sausage rolls. I watched the ANZAC day clash there. The Empire state building is always packed, best to go at night, The Rockefeller center wasn't as busy when i went, didn't really have to line up. Check out central park but be prepared to spend a lot of time there, it is huge, there is a awesome restaurant inside Central Park called the Boathouse.
SA: Buy your Spurs tickets as soon as they go on sale. Stay somewhere near the River Walk, the Marriot was good, awesome restaurants along the river-walk my favorite was called Casa Rio, very old restaurant but the food was amazing. The Riverwalk/Downtown area is only about a 20 min cab ride from the AT&T center, also try to organize a cab ride after the game with the driver that takes you in, it was a pain in the rear getting a cab after the game. Got to check out the Alamo too (which is also right near the Riverwalk)
FYI being a Spurs fan don't expect to see any Spurs Merchandise anywhere but in SA, so save your pennies to shop big in SA.
Also the tipping sucks, but if you tip you will get better service, they might as well call it a bribe, always tip BEFORE you ask for what you want. For example, I was in Vegas asked at the front counter if i could get a fridge in my room, was told "Sorry Sir we don't have Fridges" my Brother in Law asked a same thing a hour or so later, tipped the guy, "Yes Sir we'll get 1 brought up, normally its $10 a day but we can waive that" Vegas was really the worst place to tipping though, they expect a tip if they open the door for you. Most other cities were a lot better. Also leave a tip every morning on your pillow (around $5) other wise the maids will do a crappy job of cleaning your room. Always make sure you have a few $1 notes handy, they are good for tipping, kinda of awkward when you only have large notes and you need to tip someone.
Anyway i think I'm rambled on for long enough, hope its not information overload.... if you have any other question be happy to help.
Have fun!!