If you're looking for a meeting place or a good stop around ½ or halfway between Aspen and Boulder, you can try Wheeler Junction, CO, which is about 1½ hours northeast of Aspen, or about 2 hours southwest of Boulder.
Other possible places to stop near the midpoint include Copper Mountain, Masontown, Frisco, Dillon, and Silverthorne.
About ¼ or a fourth of the way, you can stop at Kobe, CO. This is almost an hour east of Aspen.
About ⅓ or a third of the way, you can stop at Stringtown, CO. This is about 1 hour east of Aspen.
About ⅔ or two thirds of the way, you can stop at Graymont, CO. This is about 2 hours northeast of Aspen, or a little over 1 hour southwest of Boulder.
About ¾ or three fourths of the way, you can stop at Black Hawk, CO. This is about 2½ hours northeast of Aspen, or almost an hour southwest of Boulder.
If you drive straight through without stopping at all, the total distance is 170 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 3 hours, 28 minutes.
