you can drive through zion via highway 9

You will then park at the visitor center close to the south entrance and take the shuttle bus to go into the zion valley.

You want to rent a SUV if you plan to drive into the monument valley rather than merely taking some pics at the visitor center. The guided tour costs $25/person.

UT/AZ is kind of the place best seen on their hiking trails. Leave some hiking time for each park will add a lot more fun to your trip, I think.

As to hotel, I found AAA's website is not bad. Lots of choices, price is fair. Sometime, hotel gives you the best deal if you call them directly.