Libraries and internet cafes are good places to check web based email services.  Your mail can appear as a web page, with some internet services, that can be accessible from anywhere.  Just be sure to remember the password. 

Following ventilation pipes into another friendly library.  This one in Hillsboro, or maybe Beaverton, OR.  I forget.

Public Libraries are great places to check email all along my route.  Also another place with a restroom and cold drinking fountain.
Sometimes there is a small wait as others use system, and/or there is something to sign, but usually the librarian gets me on right away.

On the other hand most commercial internet cafes seem to go out of business, for some reason, before I get there.

Checking email in libraries along the way.  Marco Polo would have been amazed!  Instant communication around the world.
My NW bicycle tour 2002

Photos by region, by subject, contact.