I suggest you take a direct flight to Bangkok, spend some time there and then use domestic flight down to Phuket. Thai Airways charges ~5500 baht for roundtrip but if you plan ahead you should make booking with Air Asia (
www.airasia.com) and this can get low as 1300 baht for a roundtrip ticket.
Bangkok has lot of action but also lot of traffic and the places are far from eachother, for me personally 3 days is enough in Bangkok.
In Phuket most things is within walking distance and it is more relaxed, later closing time and many activities you can do, e.g. fishing, diving, snorkeling, cabaret shows, ATV, gokart, elephant trekking, sea canoe and so on.