Based on my research, I'm going to recommend Mesa Cortina. It's a beginner route just west of Dillon (so plenty east of Vail, still.)

My sources recommend you pick up the "Summit, Vail, and Holy Cross Topo Map" which is a trail map.

Since I'm assuming you want to do this ASAP, you should either pick it up at a local bookstore or at Weber's Books, which is at 100 S Main St
Breckenridge, CO. Hopefully you can find it at a home store or have it mailed to you by Weber's, depending on when you're going. I get the sense it would be useful, regardless.

Here is a link to what your driving directions would look like if you went to Weber's books, assuming you are starting from Denver, here is what your trip would look like:
(Go to this link) http://maps.google.com/maps?f=d&saddr=denver,+co&daddr=100+S+Main+St+Breckenridge,+CO+to:ryan+gulch+rd+%26+buffalo+dr&hl=en&geocode=&mra=ls&sll=39.63462,-105.54261&sspn=0.511885,1.235962&ie=UTF8&z=10
...plus these directions, for where Google maps can't help:

"Look for Buffalo Drive on your right and TURN RIGHT here.
Buffalo Drive dead ends at Buffalo Mountain Drive and you will TURN RIGHT here.
Take the NEXT LEFT, Lakeview Drive, which is soon intersected by Aspen Drive.
TURN LEFT onto Aspen Drive and the parking lot for the trailhead will be on your right." (http://www.summitcountyexplorer.com/HIKES/Mesa Cortina - Hiking Trail.htm, reformatting and emphasis mine.)

Once on the trail, the directions are as follows:
"From the trailhead, a 20 or 25 minute walk brings you to a sign marking
the entrance to the Eagles Nest Wilderness. Soon, you begin the most
difficult part of the hike by ascending a series of switchbacks through
the forest....

[Here they recommend the book for landmarks.]

At about 2.1 miles the trail merges with an old ranching road that comes in from the right (east).

Another half mile brings you to a crossing of South Willow Creek where a sign marks the merger with the Gore Range Trail."

Stop, enjoy, and head back the other way. If you decide you want another trail, the Lily Pad trail is near by, go back to Ryan Gulch Road and take it to the very end of the road. At the end of the road there is a loop, and "At the top of the loop you will see a parking area on your left. A dirt road across from the parking area leads up the hill to the trailhead. The trail of 1.6 miles leads to two lakes - Lower Lily Pad Lake and Upper Lily Pad Lake."

Happy snowshowing, and Merry Christmas!

Here are some resources to find what you are looking for
and additional info that may be useful for traffic and weather
safety conditions for going snowshoeing:

Colorado Travel Information
including I-70 estimated travel times, weather, traffic-cams,
highway advisory radios, road conditions
http://www.cotrip.org/

41 listings for snowshoeing across Colorado by region
http://www.colorado.com/Snowshoeing.aspx?utm_source=yahoo&utm_medium=cpc&utm_campaign=national

Link to Yahoo.com discussion group discussion about snowshoeing trails
http://groups.yahoo.com/group/coloradoclimbers/message/171?l=1

put terms like I70 Colorado snowshoeing in any search engine.
Google custom search engine may be worth a try:
http://www.google.com/coop/cse/

or try Google Maps:
http://maps.google.ca/?hl=en where you get 760 results.

or Google blogs:
http://www.google.ca/blogsearch?hl=en

Creative Commons by Billingham
photo snowshoeing at Red Feather Lakes, Colorado