Papilletta
Purely due to experience, seasoned travellers know the limitations of travel - how far they can travel / sightsee for any length of time. , what to see / do, how authentic, etc.
My hunch from your question is that this is your first time to SE Asia.
My suggestion is as follows:
1/. spend about a week in a locality. 1st full day after arrival should be to 'suss' out the city / town and learn from your experiences during that day / night about how you might best enjoy the remainder of the week (or so),
2/. work out the most efficient means to travel between regions. As you have less than 3 weeks, travelling by road will consume much time. In Thailand, please DO NOT entertain night bus travel - it is far too dangerous (both crashes and robbery are more frequent than most admit). For mine, I'd fly north (Chiang Mai) from Bangkok, then south (see below) for a week or so, and return back to Bangkok,
3/. accept that unless you know where to go, how to actually get there, and can speak the local language, it is almost impossible for you to get off the 'tourist trail'. That said, even on the 'tourist trail' it is not hard to sightsee, etc., in places where many tourists don't go.
- - -
Perhaps you might look at
Travelfish . This site has more backpacking advice than any other in SE Asia.
The list of cities/towns is extensive, as is the list of accommodation.
I'll mention ideas on the basis that you'll do research at travelfish...
- - -
As indicated, spend a couple of nights in Bangkok, go away (I suggest north, then south) and a couple of nights back in Bangkopk before going home.
NORTH
Chiang Mai is both an interesting city in its own right, and a gateway for day tours, and other nearby centres.
A great day tour is
Tree Top Asia
When in Chiang Mai, try a Hang Lay (Burmese curry). You won't experience it anywhere else.
If elephant riding is your desire, perhaps the best I can suggest is to head to Pai. There you'll see a quite different Thailand. There are several elephant riding operators. But for you, maybe Thoms would be best
Thoms &
This one .
There are so many options to ride an elephant in/around Chiang Mai, but Pai is (& swimming with the elephant) is so much better. Travelling to Pai takes about 3 hours, so try and leave early and ride that afternoon before a return the next day.
You say you want to get away from the tourists. For that, I'd suggest some time in Chiang Dao. This is a VERY SPECIAL place.
Travelfish While there is elephant riding there, it aint like Pai.
I'd suggest not doing a 'hilltribe' trek anywhere in northern Thailand as it is so, so commercial. Imagine if you were a hilltribe villager, and maybe a 100 westerners pass your village each and every day. Would you want to say 'hello' or 'welcome'? I suggest not.
The trekking at Chaing Dao IS worthwhile.
SOUTH
From Chaing Mai, I'd head to either Ao Nang (via Krabi) for a western beaches experience, or the other side (either Nakhon Si Thammarat or Surat Thani ).
Ao Nang allows you to see some magnificent beaches, and visit some great islands. The snorkelling/ scuba diving is also enjoyable. But, you WILL be with hordes of westerners. That said, it can still be a great experience.
The beaches on the eastern side are much less touristy. But, transport is also virtually non-existent. The beaches just don't see too many westerners, and English is a bit shaky. At either Nakhon or Surat Thani, if you ask around you can hire either a motor bike or car. You really do need this to get around on the eastern side of the Southern Peninsular.
From Surat Thani, you can venture to Koh Samui, but this is a long boat ride. I suppose if Koh Samui is within your budget, it may be best to go straight there. But, it is both touristy and expensive.
- - -
Lets assume you've got 18 days. Then, 2 at BKK, then 8 at Chiang Mai (assuming you 'do' both Pai & Chiang Dao). Then 5 at the SOUTH (allocate 1 whole day for travel from Chaing Mai), before returning to Bangkok for 2 days.
When flying from Chiang Mai to the south, be careful which airport the flight arrives / departs. There are 2 airports. AirAsia.com uses the international airport, and appears one of the better/cheaper carriers.
Hope this helps.
Cheers
[Edited: 2011 Sep 19 00:37 - Rat on the Road:23681 - Added codes for links]
Reply to this 
