I seldom prebook hotels, and I've only been shut out once. You will find plenty of choices all along the major interstates, the longest stretch along that route with no services is between Green River and Salina UT, it's 108 miles of nothing.

Lower priced hotel chains to look at would be Motel 6, Super 8, Econolodge, Travelodge, and Rodeway. There are others. The hotels.com phone app is excellent but they don't list Motel 6 properties, they have their own app.

If I-70 is in bad shape, you will probably have to take I-25 to I-40 to get around it - which will add quite a few miles. I-80 across Wyoming is not a very good alternate, it has its own issues with wind and black ice.

To get from I-80 to I-71, you have to take I-76 for a ways.