MI to AZ is pretty vague. Northeastern Michigan to Yuma is probably an extra day of driving verus southeastern Michigan to the Four Corners region.
Either way, two days is insane for one driver. See what Google maps says for driving time, and then add a few hours onto that for bathroom breaks, meals, and gas stops. 12 hours a day is probably the high end of reasonable.
As someone else mentioned, try to pick a hotel group (IHG, Hilton, Choice, Wyndham, etc) so that you can rack up points. Most decent sized towns along the interstates have at least a couple hotels. Try to get the ones with breakfast. Whenever I do roadtrips, I prefer to stay in the smaller towns, as the hotels are usually right off the exit ramp and the rates are usually lower than in major cities.
Before you book, read reviews on the some combination of the hotels website, Expedia, Travelocity, and/or Trip Advisor, but keep in mind that people that had a good experience tend to forget to post good comments, but people with bad experiences make sure they post comments.