Depends what you want to see. If nice beaches are your thing then definitely Phuket (I would avoid Patong).
If it is temples and street food etc then Bkk is a better choice. You could catch the bus to Hua Hin to make it a two centre holiday, it's about 3 hours away.
also, don't forget you need a medical certificate from a doctor and a letter of residency from immigration too. Both easy to get for a couple of hundred baht.
If you have an international driving permit all you need to do is watch a 1 hour dlt driving video and pass a few questions. Take a screenshot of your pass grade, book an appointment and do the reaction tests on the day.
I did mine in Chaam a year and half ago, it was easy and took about 30 minutes for everything including getting the licence.
Why anyone would pay an agent is beyond me (but each to their own) and must be illegal. There are also lots of scammers offering licences, so be careful.