Here's a brain dump. I don't remember what your route was going to be/what towns you're hitting aside from Edinburgh & Glasgow, so some of these might be interesting & some might be miles out of your way.
- Arthur's Seat is a nice small hike in Edinburgh. It's a gentle hike, not too long, and ends up on a peak with a great overlook of the whole city.
- Ben Nevis is a more serious hike, but if you're in that area (it's farther North in the West, near Fort William), it's a great hike. It's the tallest peak in the UK. There will be snow at the top. For all that, it's not actually that long or difficult a hike if you have decent footwear. The Ben Nevis Inn at the foot of the trail is also a very good restaurant. (Not a great place to stay though: they're only accomodation is a bunkhouse mostly used by through-hikers.) http://www.ben-nevis-inn.co.uk/
You probably already have this mapped out, and I didn't stay anywhere very nice for the most part.