The best shops in the city centre are in and around Buchanan Street, Sauchiehall and Argyle Street, also referred to as the Style Mile. 
The area is pretty much pedestrianised with all the big brand names here and plenty of restaurants in all price categories along the way. The more exclusive stores are housed in three malls and streets off Buchanan Street. On a Saturday, especially if the weather is good the area is buzzing with activity with many an excellent busking act to put you in a good mood.
Buchanan Street itself is a stunning example of Victoriana architecture; check out the view from the steps of the Concert Hall located at the top of the street, take a deep breath and dive in. From time to time take a moment to look up and be amazed by the spectacular architectural detailing.
Shops here tend to be open till 19:00 on weekdays and 20:00 on Thursdays.