As to "where to go" - some of the campsites along the West Highland Way might be an idea. By The Way at Tyndrum is nice, there are two good ones at Kinlochleven, and I think there's camping at the Wigwams at Achtertyre as well (though I have not stayed there). People will respond that these sites can get midgy and this is true, but midges are a fact of life if you are going to camp low level in Scotland.
Actually, a small washing up bowl is quite a useful thing to have when camping as you can pile all your dirty plates etc into it, carry them to the campsite washing up facility and then use the (now clean - you've just washed up in it, remember) bowl to carry everything back again. Better than trying to wash up in some massive sink, too. Which reminds me, you'll probably want to invest in some plastic mugs, plates, and bowls.