Panera stores all over town. There is also free municipal wifi in some places, but very spotty.
Most Café´s in Mission have free wi-fi.
The Revolution Cafe at 3248 22nd Street
Mission Creek Cafe at 968 Valencia St
Ritual Coffee Roasters at 1026 Valencia St
Brainwash in SoMa
Peet's has decent coffee and WiFi but you need to ask them for the code.
Meraki is building a free mesh network all over town, but their coverage isn't complete yet (Click the link for a map).
Union Square is covered by several free hotspots.
Apple Stores. You should be able to get on their Wi-Fi networks as well as using their computers.
Axis Cafe in Potrero Hill next to CCA school. No wifi after 5pm, because they do not want to disturb guest who are having dinner, but otherwise its a great modern cafe with both indoor and outdoor sitting. Highly recommend.
Village Pizzeria on Clement & Arguello