Beth, I don't know if you have a computer mapping program or perhaps you're just not interested in getting one but it's really not needed.
I just plugged into my mapping program (Delorme) the most direct way to get from your house to Yellowstone. That's how I arrived on the 2091 miles and the route I gave. It's not necessarily a preferred route. It's just the shortest. There are many, many different ways to get there depending on what you want to see along the way.
However, if you have no time schedule you might just want to get a good road atlas - Wal Mart sells their's near the registers - and study the states you'll be passing through. Main attractions, parks, etc. are usually marked on the maps. Take a highlighter and mark things you might be interested in seeing and pick a highway that most of them are along. It doesn't have to be an interstate. Sometimes a state highway will have more for you to see and neat little towns to poke around. Many of those small towns have nice city parks for a night's stay and most of them are very reasonable in price, sometimes free.
Don't be afraid to get off the interstates if you want to really see our beautiful country. That's how we love to travel. Yes, it's slower but if you have the time, go for it. Planning the trip is part of the fun!