Free wifi, it is everywhere.
The little Eee PC is a nice little computer. Light enough to put in a handbag. Small screen is a little hard on the eyes though. I have two of them, but still prefer to travel with my large lap top.
As for wifi, you will find it almost everywhere you go. Very few accommodation places do not have wifi, most are free. Many, if not most cafes have wifi. It is the first thing I ask on entering. Many large stores have wifi, and lots of supermarkets. Often you can pick it up in the parking lot. (I am not sure if you can get a car charger for the Eee PC.) Several States have free wifi at rest areas along the major interstates. Sometimes you find it is limited by time. Other places you might find you need to pay. (I never do!)
Lifey