Plenty of cities around Denver and Boulder that have a lower cost of living. I live up in Thornton which is North of Denver by 10 ish miles, there is also Northglenn which is right next to Thornton. To the north you have Ft. Collins, Longmont, Firestone / Frederick (small, and not all to cycling friendly) Erie, Niwot, Louisville, Superior etc. I would say pretty much anything that borders Denver / boulder and in between is pretty cycling friendly. There is a great Mup system to get to different areas as well.
The rule of thumb is the closer you get to the mountains, the more expensive its going to be. For more affordable housing stick east of I-25.
You CAN ride year round, I um.. hate cold and stick to the trainer I the winter, but I do see people riding the turnpike bikeway (tracks along the Denver-boulder turnpike) year round. The road crews are quick to clear it.
I love it here, and would not go anywhere else, even if paid a lot