Here are recommendations for a ring road trip focusing on nice hikes and waterfalls. Remember to look up during your drives at night because the northern lights are known to appear on those drives ;)
The major areas where you will find great hiking are: Snaefellsnes peninsuela, Westfjords, Myvatn area, Asbyrgi, Skaftafell, Skogar and Thorsmork. However you will not have time to see all of the places and you need to plan for weather. I would recommend skipping the Westfjords because the roads there are not so great and you might have trouble at this time of year. Thorsmork can be difficult to reach for the same reason (lack of roads). But these are only recommendation and I expect you to pick what you like.
Note that you can save the recommendations you like to your own wanderlist to keep track of them.