I'm not sure you'll be able to overnight at the distillery, but you can always ask. (Remember the alcohol limit in Scotland is very low) My brother and I visited Glenkinchie, near Edinburgh, and because I was driving I got my samples in small bottles. Maybe other distilleries do the same. They also run a shuttle bus from the centre of Edinburgh.
There's several distilleries in or around Dufftown, including Glenfiddich, and a couple of campsites nearby too. I'm not an aficionado of tours, just the whisky - single malts, of course - but not all distilleries do tours, so a little research will be needed.
We visited Islay (pronounced Eye-la) last year, just after the Whisky Festival, (we don't like crowds) and stayed at the community run campsite at Port Charlotte. If you're thinking of going to the Festival, book everything well in advance. We visited a newish distillery nearby, Kilchoman, which grows its own barley, has a nice cafe and shop and produces a very good whisky. There's also a lovely beach just down the road. Sláinte