Fins and Things is always a fun trail. Great scenery and some decent challenges for a stock 60 with 31's. Some of the steeper climbs can be bypassed if the family isn't up for it. Or you could make them get out of the car and walk to the top. Kane Creek is another good moderate trail but I've never wheeled it in a stock Cruiser. The only part that you might have a tough time with is the climb out of the canyon at the end of the trail.
You always have the option of starting any trail and go until you can't make it past an obstacle, then turn around and head back out. Play around on Poison Spyder Mesa or Steel Bender. Since you bike there you probably already know that the last 2 trails are a little further away from town, so if you have any vehicle problems, it will be a hike. Then again, there is so much traffic on the trails somebody could come along and help, but you never want to rely on that.
Get the book by Charles A. Wells for the Moab area. There is a large number of trails in the book from easy to difficult and he gives a pretty good description of what you can expect on each trail.