There are four of us traveling on a tight budget, and we have three days to spend. Should we spend one in Edinburgh, then head to the highlands for a full two days and an overnight there? If so, where should we stay in the Highlands?
If I were you, I'd just go all the way to Inverness for the 3 days. Edinburgh is nice- and the castle is very good, but Inverenss is wonderful. Lots to see and do.
With only three days, you want to minimize travel time, so I would pick one place and stay there. I agree with Toni that Inverness is probably the best. There is a huge variety of things to do in and around the town. Three days in Edinburgh would also be wonderful. It's a beautiful city -- my personal favorite.