starbucks, but you need to get the code from the associate, and their stores close early in the evening. There is a store right across the SBB train station
Unternehmen Mitte, a nice bar in a former bank building
Exit SBB train station, turn left and walk about 400m to the USB building.
In the lobby you can find a free internet pc, don´t sure about wlan.
Cafe Tacuba Basel on Malzgasse1, in the old town near the Rhine. Free high quality wifi & printing. Check out their website http:/www.tacuba.ch