Matthias has an entire house for rent, about 8 km south of Rab Town, in Barbat. We went to go see it, and here is a report:
It is very private, easy to get to on the main road, with parking. You would need a car to stay here, so you can get into town, though once you got here you might not want to leave.
It is the old vineyard manager's house, abandoned and now refurbished. Rustic and romantic, it is done simply, yet with everything you need.
The house is built into the hillside so it is naturally cool and quiet, and looks over the vineyards.
You have the option of cooking in a kitchen or outdoors over open fire.
There is solar panel electricity, but no WiFi.
About 5-10 minutes walk down through the grapes you have a private pebble beach facing the neighboring (empty) island of Dolin.
Matthias is a great host, and this is a unique place to stay.
You can see the listing and reviews on AirB&B here.
But, if you email Matthias direct here, you can save money on the rental and so can he.
PRACTICAL STUFF:
Ferry timetable to Rab here.
Most people go over from the mainland just south of Senj on the car ferry. It is running continually in the summer, buy tickets when you arrive.
You can easily pick up a car in Rijeka, Split, Zagreb or Zadar. We like to use EuropCar.
See the photos below.