If you're looking for a meeting place or a good stop around ½ or halfway between Aspen and Vail, you can try Dotsero, CO, which is about 1 hour north of Aspen, or almost an hour west of Vail.
About ¼ or a fourth of the way, you can stop at Emma, CO. This is about half an hour northwest of Aspen.
About ⅓ or a third of the way, you can stop at Glenwood Springs, CO. This is almost an hour northwest of Aspen.
About ⅔ or two thirds of the way, you can stop at Eagle, CO. This is a little over 1 hour north of Aspen, or about half an hour west of Vail.
About ¾ or three fourths of the way, you can stop at Wolcott, CO. This is about 1½ hours north of Aspen, or about half an hour west of Vail.
If you drive straight through without stopping at all, the total distance is 102 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 1 hour, 54 minutes.