Dan,
Being a Denverite, I would be happy to join you at Common Ground or Riverdale Dunes two of my favorites in the Denver area. Although not private they represent the Fun in Golf.
The Private side of golf in Denver is a matter of taste, The recently done DCC by Gil Hanse is good, Cherry Hills, no introduction needed ( AP fame), I have friends that are members there and they enjoy all that it has to offer.
Pinehurst in South West Denver is a Press Maxwell Course,
Lakewood CC is a Donald Ross course recently touched by Gil and is fun to play
Columbine CC down in my neck of the woods has been recenty redone by the Reese Jones group
Bear Creek is a nice course West of Denver and on a nice evening close enough to Red Rocks to Play golf in the afternoon and cruise up to catch a show at night. Arnold Palmer design, on pretty cool land, has some realy cool holes that could even be better with some touch up.
Outside of Denver is Castle Pines and Castle Pines CC
Colorado Golf Club - Coore And Crenshaw's work south of Denver
Ravenna in South West Denver
Hiwan Golf Club just west of Denver
All the ones that I am sure you have looked into
Several other private clubs I know would welcome you but depending on the golf experince you want just go play them and see.
Cool Architecture or Cool drinks
Good Strategy or Good food.