Check out Ute Valley Park for in-town sandstone bouldering. Also, a trip out to Sheep's Nose Bouldering area in Deckers is well worth it. Tons of granite boulders to climb/explore with a short approach (5-10 minute hike). Also some sandstone bouldering in Garden of the Gods, but chalk is not allowed.
+1 for Ute Valley, really easy approach and there is info on MP about the area.
I'd also recommend Graduation Rock in North Cheyenne Canon and the Ute Pass Boulders up Highway 24 west of Manitou Springs, if you want to climb on granite.
I'd be careful up at Ute Pass- access has always been touchy. If you do go, just keep a low profile and you should be fine. Don't park at the gate (use a dirt lot further up 24 and hike up the hill). Definitely some of the better bouldering in the area though.
If you're willing to drive a little further, Newlin Creek offers some spectacular bouldering- though it'll be super hot this time of year, and doesn't offer much below V5.
Remember to stay off Garden Sandstone if it's rained recently!