You've done the rail trail. You want some place different. Where are safe places to take your little ones to learn to ride their bikes?
For the really little ones: The parking lot at LaSalettte or CCBA tennis courts.
Ice House Road, past the Mascoma Village Store in Lebanon. There's parking for the rail trail here. You can do the rail trail here or Ice House Road.
Boston Lot Trails Nature walk past APD. This section is called Sherwood Forest and has zoo animal names like Panda and Zebra. People recommend these for kids and beginning mountain bikers. The trail map is here on the UVMBA website. To get there continue on Mascoma Street and past the I89 overpass. It'll be on the right.
Wilder Multi-use Path. This paved path is one mile. You can find directions on parking here.
Buzzell Bridge Road from Union Dam to Thetford is good because there are very few people.
How about a loop around Norwich? North on River Rd. from Ledyard Bridge then up Route 5 and right up Main St. and to Huntleigh Meadows playground. Stop for ice cream at Dan and Whits afterward.
About an Hour Away
Silk Farm Road in Concord. A bit of a drive but a great place to take the kiddos. Have them ride their bikes and visit the Silk Farm Audubon Wildlife Sanctuary there too. See page 55 of this map of trails for more information.
Stowe's Recreation Path. This five mile bike path is paved. One local recommended lunch at the Prohibition Pig and ice cream at Ben and Jerry's.
For Railtrails around the Upper Valley and a bit beyond, try this list.