Mull's great! You're gonna have a great time when its not raining!
Things to do, well depending on what floats your boat (or turns your peddles), things I can recommend (from about 10 years of going to Mull every year leading field trips and various holidays).
Duart Castle and Torosay Castle (east coast). Duart is a very impressive fortress castle, whilst Torosay is smaller with a more homely feel and is great for a mooch round.
Loch Buie standing stones are also worth a visit, there are lots of standing stones on Mull, but this is a full circle.
Ardalanish Bay (on the Ross of Mull, turn left just after Bunessan and head towards Uiskin then Ardalanish. This is about the best white sand beach you are ever likely to come across, and usually almost entirely deserted.
Iona is OK, the Abbey etc are good for a visit, but I always find they are busy with coach tours and after the quiet of Mull, a bit of a culture shock. I prefer to walk in the other direction and head across to the west coast or the south of Iona, where there are some great bays and an old abandoned white marble quarry. I can also recommend the boat trips across to Staffa (boats leave from either side of the sound of Iona), and the Treshnish Isles, to look at the rocks (fingals cave), the seabirds, the seals and the dolphins.
Away from the south of the island, the road round from Pennyghael to Salem across the Burg is stunning, and there's a good descent down to the shore at Gribun. If you fancy a stiff walk, you could go up Ben More (the only Monro on Mull), but it does have a habit of being cloudy at the top, so the views, although fab, are not often visible.
Tobermory is good for a bit of shopping, being home to a distillery and a chocolate factory (let alone a thriving Balamory souvenier industry). Glen Gorm castle is worth a look at, although I think its a hotel, it is in a great setting. Dervaig is also in a lovely setting and is home to the Mull little theatre (if they have a show on its worth a visit). Calgary Bay is also gorgeous, more white sand, but then nearly everywhere is stunning!
I could go on and on..
As for camping, there are some designated sites, but there are loads of places you can camp wild if you don't mind the lack of facilities. Just make sure that is permitted in the area and if possible ask permission from the farmer/landowner first.
There's a good website for the Mull tourist board, and also the ross of mull historical society, google them and they should come up.
Anyway, have fun, I am very, very jealous!
