Kuta Lombok is the place to be for beach hopping and surfing as well as exploring the surroundings. It is home to some of the most beautiful landscapes I have seen.
This is an adventure you should not miss. It is tough and challenging and the reward on top is stunning.
The village Senaru is basically the base camp for all the hikers who want to conquer mount Rinjani. Check out the waterfalls.
Gerupuk has incredible waves for beginners and advanced surfers. Definitely worth to try. I improved a lot.
You can fly to Mataram international Airport. From there it is only a short ride by car (taxi or private driver) to Kuta, Lombok in the south where nice beaches and great waves to surf are waiting for you.
If you are already on Bali, you can also use the Ferry / Speed Boat to get to Lombok. We took the plane as it was cheaper and a lot faster.
On Lombok most of the travelers rent a scooter to get around. It is really convenient and easy to explore the island. There is not a lot of traffic on the island. Just be careful when you drive.