Shopping - for big highstreet stores Sauchihall Street / Buchanan Street / Argyle Street, Princes Square, Italian Centre, and for small boutique type shops Creswell Lane, Ruthven Lane just off Byres Road in the West End
Sightseeing - Kelvingrove Art Galleries and Museum, Hunterian Museum and Mackintosh House, Botanic Gardens (if the weather's nice), Science Centre Tower for a great view of Glasgow (if it's open!)
Food / Drink - too many places to mention, but the West End particularly Byres Road and Ashton Lane have a good selection of restaurants and bars if you don't want to roam too far, there are lots close together there, good if the weather turns nasty.
Can't think of anything else at the moment.
Have a fab time!