New York for 8 days with teen DD in June. How much to book in advance? (And top tips please)

[YoScience]

DD and I are of to NY for our summer holiday and we are starting to plan things to do.

I'm not sure of how much to book in advance, as torn between getting cheaper prices and wanting a bit of flexibility.

I have booked a show and a baseball game so far.

I've looked at the New York ass but it seems really pricy and not sure how much we would use it to get value for money

Have seen some group in deals for open top bus rides which I think might be worth it and I was going to book transportation from airport to hotel each way.

Just after advice really on whether it's worth booking other stuff in advance of playing it more by ear once we are there.

We also would like to go to Ellen's stardust diner and a trip to Coney Island.

Any other top tips or must dos(we will do Central Park, Empire State, Staten Islands ferry to see Liberty)

Yes to shake shake! As often as possible! I believe there is one in the UK now... Camden maybe?

Be careful if you take one of these hop on & off bus tours - if it is really busy it may not be as easy to hop back on as you'd like! When we went (end June) we had to wait in a long queue for well over an hour to get a bus back that had space to take us. The tour guides were mostly good though.
I didn't buy anything in advance as it seems only worth it if you want to do a lot of stuff - and we took it fairly easy.

Shake Shack in the UK is located in Covent Garden Imscarlet.

Just back from trip with kids had great time we all really enjoyed it. Budget for plenty money!

One World Observatory is now open. Would book tickets in advance.