Do you mind getting married in an iconic church along the Hudson?
If not, Riverside Church of NY's pricing is amazingly within your budget. You could contact Angela Gregory-Weddings at Riverside. There are two rooms on the 9th & 10th floors that have views of he Hudson, as well as downtown and beyond GWB. It's absolutely beautiful.
My husband have gone to and been a part of several weddings in the building and it's always beautiful. We were married in Christ Chapel, which has no view, but still beautifully romantic. You could definitely have your wedding there and stay within budget. Congratulation and good luck.
Angela's number is:212-870-6762. If you do call please tell her CharLena says hi! (And no, I do not get any renumeration.) It's just such a beautiful place AND within your budget.