Rush or lottery tickets are way cheaper than TKTS if you have the time and inclination to plan ahead. If one of you has a student id, you'll have more options. TKTS might still do $20 tickets 20minutes before the show for off broadway shows.
There's also Shakespeare in the park, which is free but you either have to line up super early or do the online lottery for tickets. The shows this summer are All's Well That Ends Well or Measure for Measure depending on the day.
For food, Eataly. The building is kind of like an Italian market with a couple different restaurants in it and some walk up stations. The gelato is to die for. It's around 23rd and 5th I believe.
Shopping, a large concentration of wealthy people make for good second hand stores. Not everyone's cup of tea but I got a Lily dress for under a hundred with the tags still on. If daughter is into fashion the Met has an exhibit on Alexander McQueen and the Cooper Hewitt has a awesome jewelry exhibit.
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