The best economy location in relation to the Rockies and Union Station involves a lot of walking. That is La Quinta at 3500 Park Avenue West, which is on the end of a long bridge that leads directly to Coors Field. It is served by RTD bus Rtes 8 and 38 to and from Downtown Denver, but they don't go to Union Station. Your group could split into several cabs and have a pretty low fare on a per person basis. Union Station has a good cab turn-out at train time.
I have heard good reports from economy groups that have stayed at the Ramada Inn at 1150 East Colfax Avenue, including the recent national convention of the Motor Bus Society. East Colfax itself bothers people who are not used to big cities, but the trade-off is that it has 24-hr a day bus service, and the Rte 15Ltd provides Limited stop service between this location and LoDo (Lower Downtown) with its many restaurants and Coors Field. The last Rte 15Ltd sets out from its LoDo terminal stop (Market/16th Streets) at 12:14 a.m. every night. Market/16th Streets is three short blocks and one long block from Union Station.
Bus routes serving 1150 E. Colfax (Colfax & Downing area) = 7, 12, 15, 15Ltd. If you prefer to play the odds from Coors Field back to this site, take the 16th Street Free Mall Ride from LoDo to the Civic Center Station end of the line, then walk half a block to the big bus stop on East Colfax eastbound. Rtes 7, 15 and 15Ltd all stop there. One-way fare is $1.75 cash.
There are some economy hotels/motor hotels on the newest Light Rail lines in the southeast suburbs, although they tend toward extended stay places. Few of these are within wallking distance of the stations. Some of them have a van for rides to and fro, but you'd have to check with them. The best-situated one is Extended Stay Hotels, Inc. at 4885 S. Quebec St., Greenwood Village, located immediately south of the Belleview Station. The E-Line runs directly there from Union Station every day of the week. Last nightly train from Union Station departs at 1:42 a.m. An additional train departs at 2:12 a.m. on Friday and Saturday nights. Union Station is in fare zone A and Belleview Station is in fare zone C, so it's a three-zone ride costing $6.00 for a round-trip ticket from the vending machines.
Hope this helps. I don't usually check this, but you can get more info from www.rtd-denver.com .