Warm Showers for Cyclists
If two wheels is your preferred mode of transportation, there is a hospitality exchange just for you. It is called Warm Showers (www.warmshowers.org) and it operates worldwide, with 73,865 active members and 27,188 active hosts at the moment.
Similar to Couchsurfing (www.couchsurfing.com,) it offers free accommodation to travellers who arrive on bicycles. The lodging can vary from a separate room or cottage to a couch in somebody's living room, to just a safe place to pitch a tent. You need to establish exactly what is being offered before you book. Since cyclists often need to repair their means of transportation, listings include the distance from each host's home to the nearest bicycle shop.
I've always admired people like the Irish writer Dervla Murphy who travel in foreign countries by bicycle. It certainly is an inexpensive way to go, and taking advantage of free lodging too would make it a huge bargain, possibly cheaper than staying home.
As with all aspects of the sharing economy, it pays to check reviews carefully before you travel.