Fun/Cool/Free: All the museums. Not technically free, they are still reasonable and you can spend days in any one of them.
The Cloisters is a monastery they moved over brick by brick from Europe. It's way up on the west side and a great place to take a date.
Shakespeare in the Park is free every year and always worth the trip. The catch? They've free, so people wait in RIDICULOUS lines to get in.
Central Park: Always activities, things to do. Very social. If you have a dog, you're set. Everyone will want to talk to you (works with babies as well)
There are a lot of affordable options too..check out <a href="http://www.nycitysearch.com" target="_blank">www.nycitysearch.com</a> or <a href="http://www.villagevoice.com" target="_blank">www.villagevoice.com</a> for more.