In reply to Fraser:
Thank you for the links to The Lighthouse and The Glasgow School of Art New Building. I am a Glasgow graduate, but have not been in Glasgow for about seven years(reunion).
In answer to the OP, I second the Kelvingrove Art Gallery as being a brilliant free place to visit. Also second the idea of going through the botanic gardens as a relaxer.(Mention was made then of eating in the Byres road area. If so in the past, The Ubiquitous chip used to have a good reputation, albeit a bit upmarket, but I have not been there for a while.) Mind you if you want to have a relaxing way of also taking in some art/style, then I would thoroughly recommend going round the Mackintosh house near to the university Library/Hunterian art gallery. It is such a lovely peaceful, light reconstruction of his house.
Just out for a view? Then consider going up the main university spire from which you can see for miles.
I am sure that Jon will have fun.