To answer your question Kiddushin 2b:
שדרכו של איש לחזר על אשה ואין דרכה של אשה לחזר על איש
As to how to save money, you indicate some dates that didnt cost anything, od more of those. Certainly over the next few weeks while the weather is still warm there are plenty free nice parks, Hi line, brooklyn bridge etc.
Lounge as yo uindicate isnt neccesariy expensive you did it for 9.52 you can bring along a game
Dating isnt free, and certainly can be expensive. Best of luck as you continue your search