There's a free wi-fi zone across the city centre. You can get a local SIM card for about a pound and data packages are cheap.
Gallery of Modern Art Basement library; free internet access. Bookings recommended.
Hillhead Library Free internet terminals.
iCafe Sip a coffee and munch on a pastry while you check your emails on super-fast connections. Wi-fi too. It's actually a very good cafe in its own right. There are other branches, including one on Sauchiehall St.
Mitchell Library Free internet access; bookings recommended.
Yeeha Internet Cafe Upstairs location in the heart of the city.