Just went about 4 weeks ago. You're in a good location as it is - Port De Pollenca is closeby and is a lovely place. A little drive northwest takes you on a fun (read: tense and breath-baiting) road to the lighthouse at Cap Formentor. There are plenty of markets going on in the main towns and the bus service on Majorca is pretty good too!
I'd recommend a day in Palma which, despite seeming a little touristy can actually be really lovely - it's a very pretty city with lots of winding streets and a lot of history. Also a lot of good shops and cafes/restaurants.
I hope the weather is better for you than it was for me! Rained 4 days out of 7...
Also you asked about getting about. I mentioned the buses but there are car rentals all over the place - the roads in Majorca are good and traffic never seemed particularly busy. Best of luck!