I can't offer suggestions, as I am just getting ready for my own trip to Norway next month. I will be staying two nights in Balestrand (traveling by train and express boat) and renting a car for one day while I'm there just to explore the area.
But I did find a great site that has some recommended driving tours, so you might look at these, see which one(s) are most appealing to you, and then pick a base that is convenient for that drive.
http://www.nasjonaleturistveger.no/en
If you're still not settled on anything by early June, ping me or wait for my trip report, and I'll be happy to give you advice based on actual experience!