I'm planning a small weekend trip with my boyfriend (2-night 3-day in
central/northern NJ or NYC area), but the forcast says it's going to
rain. My questin is what kind of activities we can do to make the most
out of the trip? We want to do some small but romantic/exciting and
memoriable activitis. We don't plan to spend too much on fancy dinners
and boardway shows. Please advise.

There are a myriad of museums to choose from, and there are historic
buildings you could tour, also.

Kriswrite

If it is raining you are in luck...walk in the rain...barefoot if
possible getting your hair and clothes wet with the nice soft water. 
If you get chilled get back to your motel and take a hot
shower...etc.!

But if it fails to rain...here's a site with lots of options...
                    http://www.fieldtrip.com/special/about.htm
                                                   :)