Our go-to websites for discounted tickets are Today Tix (www.todaytix.com) or by visiting TDF (https://www.tdf.org/nyc/7/TKTS-Overview) for the rundown of shows currently at the TKTS half price booth in Times Square.
The Yankees are in town against the visiting Astros from 6/22-6/29. https://www.mlb.com/yankees/schedule/2022-06 AND If you'd rather see some hoops than come to the Welcome Drinks, the NY Liberty WNBA team is at the Barclays Center on 6/24. https://liberty.wnba.com/
You could try one of the hop-on/hop-off bus tours like the open-top Big Bus Tours (https://www.bigbustours.com/en/new-york) OR to see our island city via water, we recommend one of the Circleline Sightseeing Boat tours (https://www.circleline.com/?locale=en)