If you're willing to head west, downtown Culver City has free wifi within a 1 mile radius around the newly gentrified blocks of Culver Blvd.
On the east side, Pazzo Gelato has free wifi and yummy gelato. It may be possible to grab a sandwich at Casbah Cafe across the street, installing yourself outside of Pazzo with one of their drinks (affogato is my favorite) Pazzo, and chow down.
3827 W Sunset Blvd, Los Angeles, CA 90026
Solar de Cahuenga
1847 N. Cahuenga (at Franklin)
Free wifi and a large selection of crepes and omelette's. It's gotten mixed reviews from chowhounders, but I had a pretty good experience there, and I've always vowed to come back and bring my laptop. Good luck.