The Henry Hudson trail that runs from Freehold to the Highlands. From the Highlands you can get on to route 36 for about a half mile and exit on to Sandy Hook. Sandy Hook offers paved bike trails and lots to explore. Back on the HH trail, it dies go through some gritty areas along the (Raritan) Bay Shore. But none that I feel unsafe in. You can extend your trip at the Freehold end by biking a couple of miles out to Monmouth Battlefield state park where there are some biking trails. Go a little further west of the park and visit Old Tennet Church. It dates back to revolutionary days and was used as a field hospital for Colonial troops during the Battle if Monmouth.
Another rail trail, the Union Transportation Trail, is being built on the old RR bed that ran from Hightstown to Pemberton, NJ. There are gaps where you have to use area roads. But it's still a nice ride. A couple of miles west of the trail you can stop in and visit Walnford, an old mill, house, stables and other out buildings that date back to the 18th century.