Depending on where you plan to go, Moab is always a wonderful place to go. White Rim Trail is very big bike friendly, and sure looks like a blast. (You can do that route in a Subaru easily enough.) Just know that it is 90 miles of off road trial, which typically takes jeeps between 12 and 20 hours to traverse.
Ouray Colorado is flat Amazing!
Vernal Utah is a beautiful place to see. Keystone, Breckenridge, Vail, Leadville Colorado etc are all great places to see.
There are a LOT of tarmac roads that are pleanty off the beaten path.
Steamboat Springs CO
Mesa Verde is worth climbing around (but they have a LOT of vertical assents and descents to tackle, so if you are not up for climbing a ladder on the side of a cliff... well.... ;)
The pass coming into Aspen is really beautiful.
I think if I were you I would start in Denver, go due SOUTH to Colorado Springs, from there take HWY24 up to woodland park, follow that through Beuna Vista (SP?) and ride on up into Leadville, or out into Breckenridge. There is much to do and see out there.
I guess the big question really is do you want just dirt, or are you ok with backwoods twisty windy tarmac?
"Do you know what a soldier is...? He's the chap who makes it possible for civilized folk to despise war."