There have been issues with shooting on public land due to urban crowding into the forest in Boulder County. (Both residence and multi use) This has gotten many areas closed.
There are ranges around but they require membership and have waiting lists. I'm guessing you are temporary and not interested in memberships. For handgun you can find range time, rifle can be dfficult.
There is Lefthand canyon, a very popular shooting area that can be sketchy when busy (But ok during the week). There is Pawnee grasslands, excellent for long range shooting but up past Ft Collins.
Check the USFS pages to see what areas are closed to shooting. Any public land not listed as closed is free to shoot. Just be very very very sure of your backstop.
Expect target shooting to be banned on public land everywhere in another month as the fire restrictions kick in. Been a dry winter so far on top of an existing drought.
