You can fly to:- 

Rijeka (40 miles). http://www.easyjet.com/. Head down the scenic coast road to the Jablanac ferry and Rab is just a 15 minute ferry ride away.

Zadar http://www.ryanair.com/ is approximately 2 hours drive South from Jablanac

Zagreb http://www.wizzair.com/ is only 2 and a half hours drive and worth an overnight stay on your way back.

Pula (Istria) http://www.ryanair.com/  is approximately 3 hour drive. Head for Rijeka and down the scenic coast road

Ljubljana http://www.easyjet.com/ is a 3 hour drive.

Split  http://www.easyjet.com/  is 3-4 hours hours south of Rab.

You'll need a car for each option and you'll need to head to Jablanac to take the car ferry from the mainland. These are regular, take just fifteen minutes.

For ferry times please visit  www.dmmedia.com/ferryplan_1hr.htm