I'd suggest the Firing Line. They have pistol ranges for members, and ranges for non-members. Plus it is indoors so you can enjoy shooting regardless the weather. They do charge a range fee, and ask that your weapon be cased or brought in with the action open and unloaded, but you can certainly go there and shoot.
I know you asked for a place that ain't a range, but aside from Firing Line, I don't know of any particular locations locally where you can just go shoot without permission. If you're looking east of Denver, the answer might be Kansas!!!