We visited the Gallery of Modern Art (GOMA) and enjoyed the architecture and stained glass.
Rogano's Fish Restaurant with it's original are deco interior is a Glasgow institution (and with a deal from Itison is affordable now and then). They serve excellent coffee and ice cream too. If you should need a hotel in the very centre of the city Grasshoppers is delighful. A room on the station side, 6 floors above the largest glass roof in Europe, was spotlessly clean and beautifully decorated, quiet and friendly with treats and a great breakfast (deals available here too).
The Mackintosh House at the Hunterian is beautiful, guided tours in the morning, self guided in the afternoons. Kember and Jones, the Botanic Gardens and Hoos my favourite little shop are all within easy walking distance of each other at this end of town.
If you know of any other special places in Glasgow I'd love to hear about them..