No, not the concert venue down in Denver, nor the climbing mecca out in Nevada. This more modest Red Rocks is a group ofvery handsome sandstone fins perched above downtown Boulder at the mouth of Boulder Canyon. It's a short hike from a couple of parking areas and offers good views of down town. The strata is tilted at 90 degrees and the rock is somewhat fragile in places.
I have no idea what routes exist here or their relative difficulty. There are some obvious lines up the larger (30-50'?) faces and chalk marks under some overhangs suggest some interesting boulder problems. The rock is fairly soft, crumbly sandstone so trad leads may not be the best idea; top ropes from gear are probably your best bet. The large, eastern-most face looks quite attractive and the top is easily accessible by scrambling up from the north.
Getting There
Red Rocks is easily accessible from either the Mount Sanitas or Settler's Park Trailheads on Mapleton Ave and Canyon Blvd, respectively, just west of downtown Boulder. The rocks themselves are easily visible on the right as you approach Boulder Canyon. Follow any of the trails up the hill and to the base of the rock.
Nope. Last year's Boulder Open Space & Mountain Parks map (see the link above) lists it very definitely as part of the the Open Space. There are official trails, an official memorial bench and assorted signage. There is a shmancy-looking community directly to the east which may be the private property you're thinking of.