By tuk-tuk[edit]
Alternatively, you can get around town by tuk-tuk (motorized 3-wheeler). this usually quoting 300 baht/hour, but this can usually be bargained to a slightly lower price (e.g., 1,000 baht for 4 hrs).
You can also flag down tuk-tuks from the street and try to hire them, most drivers carry with them a stack of postcards featuring the famous sites of the city to ease communication, they also are used to the standard temple hopping circuit. If you have a map you can point out any of the destinations that you wish to see and they'll often quote a trip price and will wait for you at each stop. 200 baht per hour seems to be the starting point for tourist tuk-tuks picking up backpackers away from the station, although it can be possible to negotiate a lower price.
If you are really determined on your route, you can negotiate a single fare with the driver. Trips from inside the island goes around 100 Baht, and from outside the island around 150 Baht. There are usually tuk-tuk outside various wats waiting to pick up passengers, so no need to worry of being stuck. They can also be easily flagged down from the street within the island.