Shady, good for hiking and appreciating the beauty of the rock. The walls are like big cavernes hollowed out from water and there are tons and tons of 90 degree walls to admire.
There may be a fine line between scrambling and bouldering. The Iowa DNR has closed this park to rock climbing. The DNR does not expressly forbid bouldering, but we can assume a land manager would probably interpret that as climbing.
From Davenport, Iowa take Hwy 22 (aka, Rockingham Road, aka E Front Street) West from the I-280 bridge.
Drive along the Mississippi river and turn right on Wildcat Den road.
Park your car where the area is marked and then hike into the woods on the path and you'll come upon large massive caverns of rock!
Free climbing, and climbing or rappelling activity which uses bolts, pitons, or similar permanent anchoring equipment or ropes, harnesses, or slings is prohibited in state parks and recreation areas, except by persons or groups registered with the person in charge of the area. Individuals participating with groups must each sign a registration form before climbing or rappelling.
Climbing or rappelling is not permitted at the Ledges State Park, Boone County; Dolliver State Park, Webster County; Wildcat Den State Park, Muscatine County; Mines of Spain Recreation Area, Dubuque County; Maquoketa Caves State Park, Jackson County; Elk Rock State Park, Marion County and Stone State Park, Woodbury and Plymouth counties
You might be able to get away with bouldering, but there's a good chance that you could get busted for climbing here. Could be a slap on the wrist, could be a fine or having your gear confiscated.
Sounds like a cool place. It's a bummer that the Iowa DNR takes such a hard line on climbing, but in their view these areas weren't acquired with climbers in mind so they have no qualms with telling us no.