Folk have already suggested the West Coast, and that has some of the best scenery. Some of the mountains rise spectacularly from the sea. Fort William is the biggest town in the area, and there is plenty of cheap accomodation if you want a night indoors for a change. Plenty of places to re-stock on supplies. You could do a 3/4 day hike from there into an area called Knoydart. Also lots of day hikes in the area, including Glen Coe. The walks can be challenging ridge scrambling, or pleasant valley walks.
Another base could be farther east in the Aviemore area. This is in the Cairngorms NP, and there is plenty of scope for a 3/4 day hike. The terrain here is different from the west coast, and is made up of high, bare plataeu, with steep sided valleys between.
It is legal to hike and camp almost anywhere in Scotland, with a few common sense exceptions. There are very few waymarked trails though, so an Ordanance Survey map and compass will be needed.
Have a look at this site for some ideas.
Feel free to contact me if i can help in any way.