Not only the library for computer access but also the employment centers have computers for public use. If you are discreet and not flamboyant, you could slip into a hotel lobby, find the computer and use it for a brief moment. If you can not find the computer then explain that you are lost and have the address located on your email. Many will help you if you are nice and promise to be quick.
Just lost trying to find a fire pit in a concrete jungle wishing it was a wooded glen...
if it wasn't for bad luck, I would have no luck at all