Determine units available.
Look at harvest statistics.
Look at topo maps for the units.
Look at satellite maps.
Look at land ownership maps.
Look at motor vehicle use maps
Narrow down some key spots that spark your interest. Ideally away from roads, and has water, cover and food.
From here contact the local biologist, ask specific questions about the areas you have identified.
Compile all the data you've found and determine which unit to hunt and further dive into the maps of where you plan to go.
Exactly what jryoung outlines X 2. Google is your friend, meaning if an area keeps popping up over and over in google searches as a top spot in xyz state it might be wise to look for an area not quite as well known. I enjoy going over the harvest/success stats and population estimates that most states provide. I also like to look at 3-5 year trends on hunter numbers, harvest rates etc. Another thing to take into consideration in the rocky mountain states is checking recent (3-5) years worth of fire and even snow pack data. Best of luck on your hunt!
You're getting some good advice here. I would add this too though. If you're muzzleloader hunting, coordinate your research questions to include where the Elk are that time of year. Around here, there are entire game management units that don't see the large populations of Elk until the weather or other factors move them into these areas. The harvest data may be decent in a certain unit, but it might be either from early or then late season hunts. If the Elk stay in their Summer & Fall ranges, it probably isn't a good idea to opt for a unit that these Elk move too later in the Fall.
Unless you are really tough, have pack stock, or use an Outfitter to get away from the roads, I'd expect to be seeing other hunters in Colorado. That's just the way it can be.