My thoughts. You decide which to play depending on how much time you have:
Commonground = 5.67/10 according to Confidentail Guide One of the most interesting public courses around, variety and great greens; terrific value at about $40.
Riverdale (Dunes) = 5/10 A bit schizoid--part Young Tom Doak and part Perry Dye, water and railroad ties. If you can stomach the latter you'll enjoy the former. Pretty close to the airport.
Plum Creek = 5/10--Pass unless you're a masochist looking for the full Pete Dye treatment.
Arrowhead = 5/10--Very pretty but if you want prettiness without bad golf go to Red Rocks Park and take a hike.
Keystone Ranch = 5/10--Mountain course 90 minutes from Denver. There are better mountain courses, including...
Bear Dance A closer-in version of a mountain course (about 45 minutes from downtown Denver). Pretty solid test and one I'd look at if a visitor looking for a mountain-type experience.
Broadmoor (East) One of my favorite courses in Colorado, classic combination of Ross and RTJ with devilish sloping greens. But I think you have to stay there (a pleasurable experience for sure) or play with a member.
Buffalo Run--Solid if unspectacular prairie course with housing that is inobtrusive. Underrated in my opinion. Very close to the airport.
Fossil Trace--If you haven't played a Jim Engh course, give this a try. It has all of the Engh quirkiness and some extras due to the quarry holes.
Green Valley Ranch-- A decent Perry Dye course, actually playable with a decent variety of holes. Home of the Colorado Open. A slight cut above Buffalo Run and I'd say comparable to Riverdale Dunes. The closest course to the airport you'll find--15 minutes or so.
Meadow Hills--Basic public golf. Not worth your time.
Murphy Creek--For some reason I haven't played this course in a long time, but as I recall it is a solid track with a good routing and variety of short and long par 4s. I don't know if housing has impinged on it; certainly not a scenic course. In any case I'd play CommonGround before MC.
Red Hawk Ridge--A not as good Jim Engh. Pass.
Ridge at Castle Pines North--A decent back nine; the front nine, where housing has encroached, seems forced. Bear Dance is a better comparable IMO.
Walnut Creek Golf Preserve--I had to look this one up as it was fka Heritage at Westmoor. For an out of towner, this might be worth a try as it has nice mountain views on the back nine, and it is a solid track that has hosted several CGA and USGA qualifiers.
Wellshire--I love Wellshire for its Donald Ross bones that still exist on some of the holes and particularly the greens, despite some destruction at the hands of the City and County of Denver. Can't recommend it for a casual visitor, however, as there are better options as recited above.