I've done what you want to do this year and have been in Indonesia, Philippines, Malaysia and Vietnam (5 months in total). As ehambers pointed out Lombok (or for the same feeling, islands of the Philippines) is nice if you like the beach - I think for me 3 months in a place like this and it would not look like paradise anymore. If I stay longer somewhere, It would be in a big city - I miss the energy if I'm staying in the mountains or the beach for too long.
If that's the same for you, then you could go to cities with great access to nature, like Yogjakarta, Indonesia, Cebu, Philippines, Hanoi, Vietnam...
On the inexpensive side: you cannot get much cheaper than Vietnam. Philippines and Indonesia while still cheap are more expensive.
I would also recommend not to stay in a hotel but to look for an apartment. I found a good apartment in 2 days in Hanoi (there's a good website for expats), it might be harder in smaller cities.
Of course, nothing limits you to Southeast Asia :-)
A good short-term apartment rental scene sounds perfect. Finding cheap flights is easy, but the housing doesn't seem trivial. 2 months is sort of an in-between duration. Too long for a hotel, too short for traditional renting.
Remember the expat website's url? A quick googling doesn't bring up any clear winner.
If that's the same for you, then you could go to cities with great access to nature, like Yogjakarta, Indonesia, Cebu, Philippines, Hanoi, Vietnam...
On the inexpensive side: you cannot get much cheaper than Vietnam. Philippines and Indonesia while still cheap are more expensive.
I would also recommend not to stay in a hotel but to look for an apartment. I found a good apartment in 2 days in Hanoi (there's a good website for expats), it might be harder in smaller cities.
Of course, nothing limits you to Southeast Asia :-)