Holidy travel sequence help please

[illinge]

I know its early days yet but I like to plan well in advance. We are visiting Thailand in June 2015 and want to visit Chiang Mai, Phuket and Pattaya (does not have to be in that sequence). We’ve been to Bangkok so don’t have to go there again but don’t mind going again if it makes sense for travel convenience. We are flying in from Australia (Gold Coast or Brisbane).

Is there any “best” or convenient sequence to visit these cities? E.g. Fly to Bangkok, get taxi to Pattaya. Get taxi back to BNK and fly to Chiang Mai. Fly Chiang Mai to PKT. Fly PKT back to Australia? I think with a stopover on route in KL or Singapore we may be able to fly direct to any one of these cities?

We prefer to fly within Thailand as opposed to taking long bus or train trips between cities.