You can easily rack up 20 miles on the bike paths through town but I'd start out heading north out of town on 36 (Broadway) to Lyons or maybe out to Longmont on the diagonal. There are lots of bike-friendly connecting roads out to the NE of Boulder. Just follow someone else since there are always lots of riders out this way. Take 9th, 13th or Folsom to the north side of town to bypass Broadway through downtown.
If you want some climbing, try heading up Lee Hill road or Lefthand Canyon. Flagstaff gets pretty steep after the turn-off to the picnic area but it is a classic ride. Have fun and be careful out there. Don't forget a pump, spare tube, water, etc.