Well there's the Glasgow Gallery of Modern art which is in the city centre, it's a nice Greek style building obviously containing an art gallery surrounded by restaurants of most types. It's also on queens street which if you follow North for a minute or so has George square which is basically an open park with a load of statues. If you go south on Queen street there's alot more restaurants.
The Gallery also connects onto Buchanan street which is the main shopping street of Glasgow.