Libraries along the trail are a useful resource. Catch up on the news. Almost all of them sell used books at very low cost. Pick them up at one library and donate them to the next. At many of them you can get on the internet to check and send e-mail.
Some libraries require a local library card, some require any library card, others are open to all.
It is worth a try to get them to bend the rules if they are not too busy. Frequently there is a small charge. There are other possible places for getting on the internet. In some places there are internet cafes, in others some other town facility has open access. This list will be updated as new information becomes available.