What part of SP? My girlfriend lives there, I leave from her house to go riding on occasion. The closest trail is Chimney Rock, though I've never been there. I plan to check it out when the weather breaks. It's easy to find your way around a new trail...just post and ask for someone to guide you, and someone will offer.
I usually ride 6 mile. It takes about 45 mins to get from "down town" scotch plains (by the police station) to the trail, but the drive is well worth it. This was the first real trail I rode and it is very fun and beginner friendly. Unfortunately it is not rideable these days due to the weather. As soon as the ground freezes, or we get a nice stretch of dry/warm weather, it will be an awesome place to go.
What to do for now? Ride the roads. Also, if you're looking for a change of pace and want to get some good distance off-road, try the D&R Canal tow path. My gf and I usually start in Bound Brook or Hillsborough and ride south. However, if I'm going to drive there I rather take the 10 extra minutes to get to 6 mile.