are there any decent but not expensive hotels near the port?

Agree with Ryan outside city and uber

Best bet would be across the river in Jersey , they have deals that include shuttles to pier

Not around that area best bet is to go outside city and get an uber in

Yes there are

Holyday inn just across of the port 48th st

I used the Staybridge. It was cheaper than most. The hotel was nice, but it is across from the bus terminal, so it is considered less desirable. It is just a few blocks from Times Square.

No it's NYC everything is expensive.

Booking app usually has good lists. Also look up hostel. Some are retreats that will lend a decent room also.