Visit Wales have an accommodation search here that you can use to search for everything from Hotels to Hostels and everything in between.
Airbnb continue to be add rooms/properties in the run up to the festival so worth checking in to see what’s on offer.
There are also other well known sites such as Booking.com and lastminute.com which may have some availability.
For info, the following towns are within 40 minutes travel via direct train to Machynlleth:
Welshpool
Newtown
Caersws
Aberdovey
Tywyn
Borth
Aberystwyth
Some independent accommodation providers offer transport to and from stations so worth checking what’s on offer a little further out if you can’t find what you are looking for in Machynlleth.