All day: Bike the 29 miles of Historic Batsto Village. Don't forget to look up once in a while, you might spot one of the eagles that live there. When you are done with the bike ride, get some dinner in the Village.
Batsto Village Home Page
All day: Go up to High Point State Park and go hiking on part of the Appalachian trail. Have a picnic lunch by the lake.
1/2 a day: Ride down to Sandy Hook and bike the length of it on the bike trail. Turn around at the Fort Hancock station and come back down the trail. You can eat very reasonably while dining at the Gull's Nest and watching the ocean. It's peaceful and pretty but a bit windy up there, so bring a windbreaker.
Sandy Hook - Sandy Hook, NJ Official New Jersey Shore site
All Day: Drive down to Chester, NJ and visit the small shops there while looking for something in particular (they have the strangest things there - pig sculptures made out of cork, steel wool lambs, antiques, odd books) and make sure to grab some food at that century-old cafe or what used to be Larison's Turkey Farm (I have no idea what it is now.). Get some homemade ice cream at the ice cream shoppe.
I Love Chester
Also, check out places you wouldn't think of like the Newark Museum
Newark Museum, the Morris County College Longo planetarium
The Longo Planetarium, the bizarre automaton collection at the Morris Museum
Morris Museum - Morristown, New Jersey and the submarine in Hackensack at the NJ Naval Museum
The New Jersey Naval Museum Hompage. The NJ PNC center had a lot of inexpensive lawn seats for outdoor concert viewing but I cannot recall if they still do that.
I was always a fan of following festivals in different towns. Down the shore, Pt. Pleasant has the Jenkinsons boardwalk, Rockaway has music at the gazebo during the summer weeks, Red Bank has fireworks and Keyport has a festival almost every weekend.
Having said all of that, if you are looking to meet people, drive down to Princeton or New Brunswick (Rutgers). There are lots of people hanging around the college all of the time, rain or shine.