If you are looking for an "full-service" Internet café where you can surf the Internet, send faxes, make copies, or print documents you can visit "The Menu Bar" which is downtown Friday Harbor on San Juan Island.
I guess they also accept UPS, US mail, and FedEx packages. They also have a coffee shop and snack bar.
I am not sure about their hours so if you have something urgent to take care of you might want to call them. Here's their website:
http://www.interisland.net/menubar/To get to this Internet café from downtown Friday Harbor just travel up Spring Street ( the main drag ) and take a left onto Argyle Avenue. The Internet shop is about 200 yards up on your right hand side. There is limited streetside parking... watch out for parking tickets.
There are a few other coffee shops in town where you can access the Internet wirelessly but I'm not sure if they offer the printing and other extras. Good luck and enjoy the islands!