As a student, I lived in North Wales and did climb Cadair Idris a few times. There are several paths up it, but I have only ever used two - the Pony Path and the Minffordd Path. The first is the longest, but I found easiest, but I would recommend the second for the views you can get (but not always due to weather!) and for the easier access down to Llyn Cau.
The path is explained most at this website: http://www.trekkingbritain.com/cadairid ... ddpath.htm
However, I would also recommend that when in Wales, you visit either the tourist information places, or local hiking places for up to date maps and local advise regarding paths and weather condition (which are not always easy to read when you visit).
When I was doing my walking in this area, the Fox's Path was the most direct way - but because of scree faces, also the most dangerous (I never attempted this, as I am not an experienced mountain walker).
May be I just have a limited sense of adventure - but I would very strongly
advise you not
to contemplate spending a night on the mountain or by the lake. The weather can change so quickly in these mountains even in the summer, and experienced climbers and walkers have died before now. Please, don't take the risk, and think of the rescue crew that may have to risk their lives to come and get you!
These wonderful mountains can demand respect, and I have learnt the hard way not to arrogantly think I would be OK and safe on them. My experience of 8hrs onTryfan when a mist came down low on a late May day taught me that in scratches, bruises, fear and blood.
If you plan to do the walk alone, it would be best to also let the local hiking/outdoor centre, hotel/B&B, mountain rescue know of your plans just before you set out. They never mind this.
Apologies if this seems too many warnings, but I hope you get to enjoy this place and the mountain in a safe way. I loved my walks on Cadair Idris, and found it less "busy" than some other mountains. If it helps explain why I urge safety and caution - I lost a friend in the Carneddau range who could not get down to safety in bad weather. Here's hoping you have a wonderful (and safe) trip. Looking forward to hearing all about it!