This is indeed the best and inexpensive way to get around the island - hire a scooter/motorbike!
You can get one from any rental shops down the street starting from 250 baht for 24 hours but my partner and I rented one from our hotel for 300 baht. Our hotel has tie-ups with rental companies nearby and its so convenient to have our bike delivered to us straight to the lobby with just a phone call from the reception. You don't even have to surrender your passport or provide your credit card number as collateral. (That's in the case for my hotel, no frills, yay!) Heck, they don't even bother to want to see your driving/riding licence. They will just ask, "You have ride before? Where you ride?" "Okay, here is key." There, mutual trust and respect among fellow human beings. Harhar.
Beware that most companies do not provide insurance for bike rentals, only for cars and jeeps, so your travel insurance back home may not cover any accidents.. Ride at your own (but sensible) risk... Check the bike before you go and take lotsa pictures of it as evidence. Go over any existing damages already on the bike with the vendor. Btw, the bike company we dealt with were honest and helpful so we were not scammed. 150 baht for a full tank( 2 litres for 125cc auto scooter) from the company is daylight robbery but heck, we took it for convenience's sake so that we do not have to top up before we set off.
Note: Gas is sold any many shops along the streets ( in yellow, green and red steel drums or yellow and orange bottles) for 40 baht a litre. so full tank would cost ya only 80 baht... Top-up at gas stations- much cheaper!! The cheapest and I guess lowest grade petrol costs only 31 baht a litre! A bargain! A full tank will last you a ride around the island for the whole day... just don't accelerate and brake like a mad person ( i did) and waste the gas.
Be careful when navigating the streets. Always wear a helmet ( who cares if you look dorky, you'd want to live to see another day!!) and ride on the left side of the road if you are less confident. Other mad motorists like farangs (caucasian tourists) and locals will speed past you but most polite ones will toot their horn at you to warn you that they are overtaking. Such courtesy! Zero road rage! Watch out for portholes, cracks, water puddles, sand and crossing animals on the streets. The pedestrians are not as suicidal as those in Bangladesh, Vietnam, Bali even Italy when they cross the busy streets. They wait and cross... patiently and politely. Thats because the motorists here are polite as well and are never out to kill or knock down anyone - they slow down way ahead in time.... here I am raving about Thai traffic.....
If you get lost, (which my bf and I did, trying to ride home at night in the monsoon rains), ask for help at the Police Stations (we stopped at Bophut Police Station), ask the security fellas at the luxury resorts or as a last resort, stop at any convenient store. Chances of them being able to speak some English and direct you is much higher than if you were to stop and ask any passing local... Bring a map with ya because it would be your own navigating bible. No GPS here...