I go to a few different ranges depending on where I am at.
The closest to downtown that I know of is the Silver Bullet.
They are on 38th west of Sheridan (not that close, but about 10 minutes from Park Ave.). Usual price is $10 per hour for members & $15 for non (general Public) you get discounts for LE as well. Afternoons they are not too busy.
The Firing Line is decent & K2 is not bad either and usually not very full.

You can always Google "Denver indoor shooting range" or something like that, and get plenty of details I am sure.