I'm envious. The CZ is a neat trip, and Colorado is a great stopover on the trip. Here's a couple of thoughts based on several trips we've made to the area...1. Denver has several rental car agencies with downtown offices - know for sure Hertz and Avis have locations, Enterprise may also. All are located a few blocks away from the station, but will pick you up. When we rented from Hertz, they were open on Saturday morning when we arrived, but when we dropped off a week later on Sunday, they were closed in the evening. Still, were able to drop the keys and leave car in lot by the building. Denver is probably the most affordable rental car location on this trip.
2. Winter Park / Granby would enable you to see the front range by train, but will leave you off in a akward location, road and rental wise. Granby used to have a rental agency in town (think it was Avis, but don't hold me to it), but it'll probably be more expensive than the Denver option. You'll also need to go back on US40 over Berthoud Pass to pick up I70, then go west to Brekenridge. Not a bad drive, but you'll drive as much as you would if you had started off from Denver.
3. Glenwood Springs may be another option to consider. There are rental car agencies in town (not sure which ones - might try yahoo yellow pages), and Glenwood would enable you to see the neatest part of the CZ route through the Rockies (assume you're traveling westbound on the way out, eastbound on the return). Glenwood has a nice manned station, convenient hotels, and a really neat outdoor hot springs pool that's worth a visit. Be warned however that you'll be backtracking on I70 to get back to Brekenridge.
Another option in Denver - there are several shuttle bus services which run scheduled trips from Denver's airport to all the ski resorts. If you wanted to avoid a car rental, you might want to investigate this option. I don't have specifics, but you may be able to call Denver International Airport information, or go through a travel agent to get details. Shuttle buses run to the major resorts on the I70 corridor and also Aspen.
Good luck, and hope you have a great trip.