Hi, Sue,
I don't know how much time you're really going to have to spend in Glasgow. If your flight from Dublin arrives at 11:30, you'll still need to collect your luggage and catch the express bus in to town. I'm not sure whether you have to clear Immigration coming from an E.U. country. Perhaps someone who has taken this flight can clue us in.
If it's just luggage and the bus, it's probably going to be around 1:00 p.m. by the time that you get in to center city. The bus will drop you off at George Square (as featured in the movie World War Z). From there, you can easily walk to Queen Street Station to stow your luggage. This will probably take about another 20 minutes or so. Now you're looking at close to 1:30.
I'm not sure what time your train leaves for Edinburgh, but they run on a very frequent basis. You probably don't want to leave Glasgow too late in the day, as you'll want to get settled in to your accommodation in Edinburgh.
Most of the sites in Glasgow are not near Queen Street Station. You need to pick one site to visit, possibly two which are close to one another. I'd plump for Glasgow Cathedral and the Necropolis. Both are within walking distance of Queen Street Station. You could also combine those two with the Saint Mungo Museum, which is close by. Unfortunately, their cafe is currently closed, but could be open by the time you arrive. If you want to visit just one big museum, the Riverside would fill the bill. There is something for everyone.
Don't forget that you're going to be hungry after your flight and the bus, so you're probably going to want to get something to eat. If you are in Glasgow on a Saturday or a Sunday, you may want to visit The Barras, which is a Glasgow institution unlike anything else in Scotland. If you do go to The Barras, be sure to keep a close eye on the youngster.
If you want to avoid museums, and just enjoy central Glasgow, you could visit the "shopping Z", which consists of Argyle Street, Buchanan Street, and Sauchiehall Street. There are shops, both independent and chain, galore; lots of restaurants; buskers; and an opportunity to see the heart of Glasgow in all its litter-strewn glory. You could also include a visit to the Gallery of Modern Art, on nearby Queen Street. Be sure to check out the iconic statue of the Duke of Wellington in front of the Gallery, and take note of his unique headgear.
That's it for starters.
Mike (Auchterless)