Because the distances between villages and spots are quite big, you will definitely need to rent a car. It is best to make a reservation on the internet and then pick up the car on the airport (search on Auto Europe for the best prices on your travel dates). If you make your reservation early enough you can get great prices from 10-15€ per day. The gas compared to the rest of Europe and even Spain is cheap; it's around 0,70-1,00€/ltr.
As I am into skateboarding too, I went to La Olivia several times. They have a super nice bowl to practice turns on a carver skateboard.
If you would like to get an overview of the island, one of the volcanos is a must! The best one is the one next to the village Lajares. It has a big crater and a great view over the island!
Even if you're not into surfing, you can do many other things on the island. Like Snorkeling on Lobos, climb the volcanos, go to Cotillo beach to eat in yummy restaurants. My favorite is La Marisma, they serve a variety of fish and paella (rice with sea food).
Don't expect big cities, these are small villages, but they make the island so charming!