Thailand forum

Some of your asks are a bit mutually exclusive - get a place with good bars and there's likely to be a fair few students. And you can't discount students anywhere - that's the luck of the draw.
And the culture thing - not too many island/beach areas have it. Phuket would be best for temples, architecture etc. Really quiet islands like Ko Kho Khao , Ko Phra Thong, Ko Sukorn and Ko Libong are maybe best to see island fishing/farming lifestyles not too impacted by tourism. Ko Jum and little Ko Chang Andaman side are not bad either.

Okay, islands which meet most of your other asks and where I've seem fewer student age travellers:
Ko Phayam - for party you are maybe best located on Ao Yai beach.
Little Ko Chang - more laid back and tending to draw the older long term laid back traveller types. Last time I visited Ko Chang Resort on Ao Yai (another one) was finishing a new bar and there is another just north on the beach. An excellent island for treks.
Both Phayam and adjacent little Chang are easy to reach from Khao Sok - catch a bus west to Takua Pa bus station and change for one to Ranong. Ask at the bus station for the pier to these islands. Kiwi Guest House at the bus station can book you accommodation and take you down to the pier - but a motorcycle taxi will get you there and this time of year there will be no problems finding walk in accommodation on the islands.
With 2 weeks I'd be spending time on both islands. As a matter of fact I'd be fitting in time at one of the quieter* islands a bit further south like Ko Phra Thong, Ko Kho Khao or even the Similans or Surins.
* not that little Chang is noisy or busy. It tends to have a serene atmosphere.

Further south again - if you stayed on the south end of Andaman Beach on Ko Jum around New or Joy bungalows you would probably be happy. For a second location you could hop the short distance to Ton Sai at Krabi - the climbers' beach. I'm not too sure how many climbers are students but I always find the atmosphere interesting. The treks across to and around East Railay are good, enough little bars and restaurants. Big on scenery, not on culture.
Ko Lanta is nearby - I reckon old favourite Lanta Marina on Long Beach might be the go. Nice beach, plenty of nearby bars - can't promise no students though. Lanta is one of the more popular islands.

I've been to Thailand in 2005 and here are the places I visited:

1. The Grand Palace in Bangkok
2. The floating market
3. Samphran Elephant Ground and Zoo
4. Noong Nooch Village
5. Bang Pa-in Palace
6. The Ruins

I also visited some temples. My friends told me that Phuket is really nice, I didn't get a chance to see it myself because when I visited BKK, Phuket just experienced tsunami. Enjoy the rest of your stay in Thailand.