As Old Guy says, wi-fi is getting to be ubiquitous. If your supported tour stays in motels, it's usually safe to bet there'll be wi-fi. If not, well, you'll pass through a town every day, so you can find wi-fi at libraries, many restaurants, coffee shops, etc.
If you want to surf from a tent or picnic table, you'll need to get a wireless plan and pay the cell company (through the nose!). Most of the time you'll be able to get a cell signal east of the Rockies, except in a few rural parts of the Appalachians and Ozarks. It's usually cheaper to get a wi-fi device to plug into your laptop (do tablets support these? I don't know.) Verizon, at least, will let you use a smartphone as a wi-fi base, but you'll pay a hefty premium for that "privilege." Verizon seems to have the best rural coverage, followed by AT&T, with T-Mobile (one kid called his "T-Maybe") bringing up the rear.
Some people call me cheap, but I'd stick with your voice and text cell phone for calls, and take large netbook for web access. You might want to save a pound and take a tablet, but a large netbook's keyboard fits my hands best.