Had a fantastic meal at Eataly on a recent visit: http://eatalyny.com/
If you haven’t been before then it seems a bit odd – you feel like you’ve walked into a deli/supermarket but fear not. It has separate sections for starters / pizza and pasta / fish / veggie / desserts. You need to book a table where you want to eat.
The food was (imho) extremely good and the desserts were something else (look out for the salted caramel ones in particular).
Other than that we just did all the touristy stuff so can’t help with the more creative things to do…