A nice idea would be to go to the Bronx, do bikur cholim by Montefiore Hospital, have a bite from their cafeteria, which is KFP, under strict hashgacha and very reasonably priced (you can get two meals for under $15 there), and then go to a nice place, like the NY Botanical Gardens, or the Bartow Pell Mansion.
I was at the Met game yesterday with my family. Sitting right in front of us was an unmarried couple. Seems like they both were having fun. Tomorrows game is also in NY and the weather should be fine. Take blankets for the end, it does get cold in the stands this time of year.
How about the ferry to Staten Island or Governor’s Island especially after dark although I am not sure if Governor’s Island is open after dark or the Tramway to Roosevelt Island. Also you can go to the NY Public Library 42nd St. and 5th Ave, the reading room are like a museum with paintings on the wall and there are places to sit and talk.