With only one day, you are somewhat limited in how much you can get in. Arches is nice as there are many easy hikes the boys can enjoy like Park Avenue, hanging around the Windows Section, Devil's Garden maybe. If you do a Jeep or Hummer tour, look at doing something on Hell's Revenge, which is close to town and full of thrills.
Hampton Inn is a few blocks north of the main core of downtown. If you like Mexican, Hacienda is easy walking distance right next to Lin Ottinger's Rock Shop - definitely take the boys there. Sweet Cravings is a small breakfast/sandwich show also close to the Hampton. Moab Brewery or Zax are also fun spots with kids.
I'm not sure I would recommend biking. You really don't have time. And there's nothing all that unique or interesting you can realistically do with their age group other than ride around town, which is great, but you'll get a lot more out of your time if you hike in Arches and take a Jeep or Hummer tour.
Edited: 12:36 am, June 19, 2013