I have a similar job (can telecommute from wherever), but with a wife and young son I'm not quite as flexible as you are.
Have you considered a kind of hybrid bike/van setup? Get a van to use as a base camp, drive it to an area you want to explore, and then do day rides or multi-day rides, returning to the van to resupply, sleep, etc. While you are out biking you can park it on a safe-looking street or in a long-term parking lot. There are a lot of resources on the Web that cover this sort of thing.
You might also consider the national and international network of hostels. Most have maximum stay limits, probably a week or so. There aren't as many in the USA as there used to be, but internationally there are quite a lot. See http://www.hiusa.org/hostels/usa-hostels
For Internet access you'd definitely want your own "MiFi" cellular hotspot so you aren't reliant on finding free WiFi. I've used both T-mobile and now Verizon 4G devices and they work well, even with VPN.