RM 1k, u def could go many places for 1 week ... go thailand ... khaosan bckpacker heaven ~ last time laa ...

Might as well BKK + CHiang Mai on train ...
Here's my elaboration.
KL or which ever part to BKK - usually an overnite train, go the 2nd class aircond bed enough, preferrable Bottom

Accomodation, for solo, usually go and search for some hostel, no need to be in khaosan, really. (The only thing is RM is low to Baht)

Food, eat of the street hawker.
Transport - do home work and use the BTS + Walking / Tuktuk (beware the scams) or Boat, you will go places. I usually stay near the place I mainly wanna go.

BKK - Chiang Mai is the same overnite train. So for the trip, you would spend like 4 nites on train (back n forth)

Chiang Mai is actually cheaper if you are going duo, solo ~ it would be slight same price for getiing 2 pax.

On the way back, if u have the extra cash, you could try 1st Class cabin room on the train ~ something we dont get to do often ...