Welcome aboard the RoadTrip America Forums!
Four days is just a shade more than you'll need for this trip, so you will have some spare time to get off the straight and narrow. And there's no reason why knowing where you're going to bed down each night should seriously impinge on your ability to explore a bit. Indeed, knowing that you've got a warm comfortable room waiting for you at the end of the day could open things up a bit since it's one less thing you'll have to worry about.
So, first a route. I'd highly recommend that you ignore what most software will tell you is the 'best' route (I-90/I-80, lots of big cities and tolls) and instead dip just a bit farther south taking I-84 west out of Hartford to Scranton, I-81 down to I-80 across Pennsylvania, continuing straight onto I-76 rather than following I-80 onto the Ohio Turnpike, dropping a bit farther south on I-71 to Columbus and finally I-70 the rest of the way to Denver. You'd have to cover right around 500 miles a day which is a nice easy pace. Overnights would be in or near Du Bois PA, Terre Haute IN, and Salina KS. Those are all fair-sized towns with multiple lodging options.
Another advantage of going the I-84/I-80/I-70 route is that there are parallel 'back' roads that you can use to break up the monotony of freeway travel without it costing too much in time. US-6 is an option in northern PA although I-80 is a scenic route in its own right. US-40 runs next to I-70 through western Ohio, Indiana and Illinois. US-50 is an option in Missouri as is US-24 in Kansas. You can't use all of those roads but you can pick and choose where you might want to see a bit more than you can from the Interstates, or simply travel at a slower pace for a while.
AZBuck