Glasgow is an up-and-coming city with a lot going for it - fairly vibrant city centre, and various galleries, museums, etc. dotted around. The armadillo-shaped science museum and the Kelvingrove art gallery are worth a visit. Try some of the local 'delicacies' - haggis, chips and gravy/cheese/curry sauce, battered Mars bar! (But not too many!)
The accent may take a little getting used to, though!
Also, try to get out of the city and to the west coast if you possibly can: Oban, Ullapool, maybe one of the islands. And if you can get north a little into the southern mountains, they're definitely worth a trip. Much of the scenery is breathtaking. I'm sure there will be tours available (like a day trip or 2 days) if you have a look. Try going to visitscotland.com for more details.
If you're stuck, give me a shout.