If you get a recommendation for someplace you might like you should make a reservation. Opentable.com can be searched by date (ie Nov 22) and location (ie Manhattan) and will show which ones are open and have seating times available. I would reserve early.
As far as getting around, I always had good luck with the subway but that was most recently 6 years ago so maybe it has gone downhill.
I think a cab might be cheaper than Uber if Uber has surge pricing during the Thanksgiving holiday but I’m not sure.
I guess you could go to the mandatory Macy’s Thanksgiving Day parade. Other places I have enjoyed are top of the Empire State Building ( but I heard it is more crowded with longer lines and expensive than when I went), Top of the Rock and Rockefeller Center, Statue of Liberty, Central Park. The Intrepid Sea, Air and Space Museum could be of interest. I think they are closed Thanksgiving Day but should be open the day after. Of course there is always plenty of $$$hopping available.
Link: https://www.opentable.com/s/?covers=2&dateTime=2018-11-22%2019%3A00&metroId=8&enableSimpleCuisines=true&includeticketedavailability=true&pageType=0