What kind of cities and hotels do you like?
What route are you taking?
Please help us help you.
Denver to Boston is a 30 hour drive according to google maps. And, yes, Chicago is about half way. So, if you want to do this drive in two days, you have two 15 hour days with a stop in Chicago. If you want to do only 10 hours a day it will take three days. Stops could be in Des Moines (as mentioned above) and Cleveland. Only about three hours out of your 30 hour trip is in Colorado.
If you just want to see where to stop on the fastest route, just put Denver to Boston in google maps and look for cities at you time limits for each day. Then look at reviews for hotels in those cities. I've only been to Chicago once and that was one night. Never been to Des Moines at all. If you're looking for interesting places to stop along the way post in the road trip forum.
You are going to need a couple nights on the road, It's not realistic to make Chicago from Denver. As Babalax noted, Des Moines is a good functional stop. We do versions of Rockies to midwest a few times a year. Des Moines is a frequent stop or the Lincoln/Omaha/Council Bluffs area, You'll find options from every major national chain hotel along I-80 in that area.
As noted, go to Google Maps and plot it out.
I think we will do it in three days.
Day 1....I'd personally push on to Iowa City. Fun, highly walkable, college town with cute shops and restaurants. Depending on how you drive, you can make it in less than 12 hours. I don't know if you like B&Bs, but the Burford House is close to the action and I saw rooms for $89 that included a sit-down breakfast!
Day 2.... What about staying in and round Cuyahoga Valley National Park? About a 9 hour drive and might be a good place to do some hiking and stretch your legs.
Day 3... into Boston.
We are planning our trip from Taunton to Denver in September to visit my sister. How was your trip? What would you recommend or definitely avoid? We are very slow travelers, plus we don't have a deadline.
Hope to hear from you!