I would agree with the visits to the Hunterian and Kelvingrove Museums.

At the risk of being too touristy, I would still suggest a trip on the HOHO bus to get a good overview of Glasgow - and you can stop off where you choose for a deeper visit.

I would also add that you might like to visit The People's Palace - a very interesting and hands-on museum depicting Glasgow's past, and then have some refreshments in the attached Winter Garden. You should also visit The Tenement Museum - slightly off the beaten track to see what an authentic flat of the 1900s looked like.

Have a great time.