Hello
We've stayed in a couple of places on Koh Phangan and Koh Samui. Personally I much preferred Koh Phangan, Koh Samui is much more commercial - McDonalds, Starbucks etc. However for a few days it made a nice change to be back in civillisation but without sounding
w@nky, it's not really 'proper Thailand'.
Chaweng Beach is by far the most touristy beach (but probably the best) on Koh Samui, we stayed right at the north (quieter) end though in a place called The Island which is definitely more suited to a 30+ years flashpacker
We also stayed in Bo Phut on Koh Samui, the beach wasn't as good there but it was a much nicer area to stay - lots of really good little restaurants etc. We stayed in a place called Smile Resort there which was lovely.
You probably know this but on Koh Phangan don't stay in Haad Rin (where the Full Moon Parties are), although a FMP is definitely worth going to, and the aftershow at Backyard is really good.
We have stayed in Ban Kai (about 3 miles outside Haad Rin) a couple of times, in Bankai Orchid resort - highly recommended and attracts a more mature clientelle
if you don't want to be surrounded by lots of gap year students.
To really get away from it though I'd recommend going right up to the north, we spent a few days on Thong Nai Pan Nio beach (bit further around than Bottle Beach) in a place called Baan Pan Buri and just totally chilled for a few days. If you are going to head north the roads up there are still essentially tracks so it's not that easy to get about but if you just want to chill then I'd head up there.
I'm not sure how long you have got, personally I'd do just 3/4 days on Koh Samui, maybe a week somewhere more accessible on Koh Phangan like Ban Kai/Ban Tai and then finish up right up on the north of Koh Phangan for total chilled-ness.