My info may be a bit out of date, but.... Renting a motorhome is generally way cheaper then rental cars and hotels. A medical type fellow who was based in Anchorage and spent a day or two on the Kenai with an overnight weekly was telling me the hotel was $79 in January and $250 in August and no rooms available. He had to move to a lesser accommodation miles away from work. For the peak summer season a motorhome looks to be about half the cost of a rental car and hotel/motel, if you can find a room.
One nice part about Alaska in the summer is that there are a lot of places to camp. Reservations are only needed for Denali and Seward on the 4th of July.
For a one week trip, pick an area and spend your time there. Constant driving to get from one place to another is not a vacation.