The problem with answering a question like that is that you can keep going on & on - how many days is multi day? could be 3 days, could be a couple of weeks
However, a good start would be to look at north west Scotland, say from Loch Stack & Arkle to Richonnich then the area from the A838 west & north to the coast, around Sandwood Bay and Cape Wrath, Kinlochbervie
OS 1 : 50, 000 sheet 15 covers it, Search YouTube and Google for Cape Wrath etc
There are a few bothies in the area; and I hear that the high lochans are some of the best wild camping sites in Britain
A few years ago I walked from Strath Carron to Cape Wrath via Kinlochewe, Ullapool, Kylestrome, & Richonnich, and met hardly anyone in the hills