Here it is, it's called the Firing Line. It was pretty well run when I went there, but that was 20 years ago.
http://www.firinglineonline.com/It's probably a good 15 miles from Downtown Denver. The pistol range only goes out to 40 ft., but they used to have a nice assortment of guns to rent - great idea if you want to try first.
REI is in the old Forney Museum. It was an old transportation museum. If you like old buildings, you'll love it.
Just walking around Denver, there is some very cool architecture if you like that sort of thing. Go down 17th street, some very ornate buildings. At 20th and California, there is a skyscraper built around Holy Ghost Church. The columns in some places come within 6 ft of the Church. They had to get permission from the church to swing the crane over it's airspace, so the pastor at the time had them give a donation to the homeless in perpetuity every year. And they still do. I used to work in that building.
Ok, I'll stop now.