While not as strict as Riyadh, Jeddah still falls under Islamic law. Read, understand, and follow the guidelines in the Saudi Arabia article to stay out of trouble.
Local women normally wear a hijab headscarf and abaya long black overgarment to cover their heads and entire bodies. Abayas, not only hijabs, are also required for Western women, however, this is not strictly enforced.
While you may be able to find alcohol at private parties, it is still forbidden in Saudi Arabia. Corporal punishment for Westerners is rare, but it has happened on occasion.
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Most shopping malls have Internet cafes. Coffee places such as Costa Coffe, StarBucks Coffee, Barnies, Second Cup and many more provide WiFi access to customers.