If you like Indian food, I really think you can't beat the Mother India Cafe just opposite the Kelvingrove museum. Indian Tapas! It's brilliant but doesn't take bookings, the queue can be out the door but it's worth the wait! We also like Firebird, just down the road from there.
Museums are good (and free!) - Burrell Collection in Pollok Park, Kelvingrove, People's Palace, Tenement House, Museum of Religious Life and Art, Provand's Lordship (oldest house in glasgow) and Scotland Street School. Centre For Contemporary Arts, the Tramway and The Lighthouse can have good exhibitions, and Glasgow Film Theatre sometimes shows some really quirky or old-fashioned films. If the weather is good the Botanic Gardens and Kibble Palace are nice.
There are some good pubs especially in the West End, several often have ceilidh music (some with Gaelic names can be good). I'd avoid the city centre at night on a weekend unless you're into clubbing and stuff - it's not unsafe as Glasgow is a friendly place but it's just full of youngsters getting wasted especially on Sauchiehall Street!
Hope you have a great time, we love being weegies!!