The ' House for an Art Lover ' in Bellahouston Park is a beautiful building based on a Rennie McIntosh design , the Peoples Palace is full of artefacts and stories about Glasgows history.
If you like architecture I would just go for a stroll round Buchanan Street, Royal Exchange Square and Sauchiehall street and look at the buildings above the level of the shops. Lots of lovely old sandstone buildings with nice wee touches easily missed by those hurrying along and staring straight ahead.