Most any laptop these days will have built in Wifi. It will get you an internet connection at campgrounds, marinas, motels, urban areas, etc. WiFi is often free but generally not very secure so shouldn't be used for banking or things like that. Some places do charge for it, it just really depends where you are.

Cell modems are also available from Cell phone providers. You just plug it into the laptop and then you can get an internet connection anywhere there's cell service. That usually covers a broader area than WiFi and gets to some more remote locations but not still everywhere. The big bummer with those is that it requires yet another contract with the cell phone company which treats them as just another cell phone. So you get another 2 year monthly payment on a contract whether you use it or not.

I'd start with built in Wifi and see how it works for you. Some places might gouge you for $10/day to connect but others are free so you just have to look around.

I know you don't want an iphone or 'droid but that might be the easiest way to stay connected since they have WiFi, cellular internet, and a phone built in