You could try: Slaters on Howard Street; House of Fraser on Buchanan Street; The Italian Center on Ingram Street if you're feeling flush; John Lewis in Buchanan Galleries. I would stay away from Sauchiehall street, as it's pretty much just pound shops and other tat, which is a shame as it used to be good.
I have to confess I bought my last suit in Next, so perhaps I'm not the best person to advise you. Oh, and it's pissing down. Good luck.