OK, forget Cadair Idris. This is close by, better and less people, also "higher"!
Go to Dinas Mawddy and up the Cywarch valley to small carpark (with toilet) at SH 853189. Climb up the gully (marked as FP on the maps) and then on up to Llyn Fign on top of Glasgwm. Camp - water OK in the lake but should be full of frogs!
Next day walk back down Glasgwm and along the ridge to top of Aran Fawddy, enojy brilliant views etc. then back to carpark via the memorial stone at Drws Bach at 863213 and east flank of the Hengwm valley.
You could extend this if you like along the ridge etc. depends on the day. Check grid refs - done in a bit of a hurry.
I agree with Waldo (as another LDWA man), it isn't too hard if you want to do it enough, but you haven't left yourself a great deal of time to prepare - and we don't know your age, job, commitments etc. etc.
Basically, get as much time on your feet as possible (every little bit helps, even an hour after work) and do long walks every weekend. Carry an overweight rucksack, train on the route and if you can do 25 miles you will manage 40 on the day. Be prepared for up to 20 hours if you aren't experienced and self supported, this also gives you time for a quick pint or two if you pass a pub on the day!
I agree with Kate about the Elan valleys, but if you drive to Beulah and then take the little Abergwesyn road there are a number of nice approaches to Drygarn Fawr ridge from the south. It is easy to make your own route once you have the OS map and from there you are highly unlikely to see anyone all day! It avoids all the visitors from the main Elan valley centre and a quick drive from Builth.
There is also a little forest café at Nant yr Hwch, grid ref: SN 883543.
If you make it to the top of Drygarn give me a wave!!