Anywhere. Best way to do that is to check the rates nearby your place and rates in downtown. Than make a final decision. Despite of all vehicles have full insurance it works only in case you have Thai (or international) driving license entitling driving certain type vehicle. Any other type driving license wouldn’t be accepted in Thai court.
In case someone bumped you not to hard owner would repair car by himself, using the insurance, but in case of car accident with presence of police, your non-Thai and non-international driving license wouldn’t work same as full vehicle insurance. And keep in mind that presence of alcohol in your blood denies any insurance.
Don’t forget to check pass inspection. This is square paper 10x10 sm with lot of Thai text and big numbers matching the year. For example 2555 is 2012 A.C. Check the expiring date. If police stop you first thing they would do is to check your driving license and pass inspection. If you don’t have pass inspection police won’t let you away until obtaining information with the owner.
Always wear helmet if drive motorbike. Absence of helmet is 80% of all fines in Thailand.
It’s necessary to make photo of vehicle from all perspectives, in presence of the owner.