+1 on the Gore Range.
Besides being beautiful, this area has the added benefit of several "exit" points to Dillon/Silverthorne, Frisco, Copper Mtn, etc. meaning that if something happened or someone got altitude sickness, you could get out or get help a little easier than more remote places.
Although I did a 3-day years ago going S-to-N, you could try leaving from North Rock Creek TH (off Hwy 9 from Silverthorne), follow the Gore Range trail roughly south to Copper Mtn, have a cheeseburger and beer at the ski lodge, and then follow the Colorado Trail back towards Keystone or Dillon. Easy I-70 access for your friends/family to pick you up and drop off.
Try this map for a detailed overview of the entire area: