Welcome to the RTA Forum!
First thing to note, I-80 could be a fine choice of a route, as could a route through Colorado and Utah, however I-80 doesn't go through either of those states.
Really, there is never a one sized fits all best route, and the best advice I can give is to pick a route that takes you to the places you want to go. If that is Colorado and Utah, which have more than a dozen great national parks, and tons of great places to go and things to do, then that's where you should go! 10 days for this trip is a nice amount of time, as you're looking at about 5-6 full days of driving, leaving you another 4-5 days just to explore and have fun.
Having said that, we really don't know what you'd be interested in doing, and no one really can know that better than yourself. With millions of possibilties on a cross country trip, you need to take the first step to figure out your top priorities (which is really the fun part anyway). Once you've established a few ideas, then we can help you sort things out and perhaps offer some additional ideas that would compliment your goals.