I once rented a bike from University Bicycles in Boulder for a week for a visiting guest.

For an introductory canyon climb, you might try Lefthand Canyon, just North of Boulder.
The reason is that it is only 4% until you get to the last mile just before Ward when it briefly hits 12%.
14 miles from US36 to Ward.
(You might just want to turn around at that point.)
It was all just refurbished last fall, (due to damage from the 2012 floods).

Now if you can handle a sustained 6% grade, Lookout Mtn (overlooks Golden) is much more scenic.
5 miles from Hwy 6 to the top, then you can keep going over rolling terrain paralleling I-70.
When you reach the intersection of I-70 & Hwy40, you can pick up the brand-spanking new bike path that continues West.
This new path on my "to do" list since I have not done it yet.