I don't really need to use library computers, I just like to sometimes. I've actually got my own laptop with a little wi-fi antenna. I've picked up free wi-fi at Burger King, Staples, Best Buy, coffee shops, hotels, Subway, Hardees, Panera Bread, etc. Lots of places have free wi-fi. If you want to scope out where you can find wireless internet in your area or where you are headed, check out these terrific websites.
(FREE wi-fi locations - Either click on the categories, or scroll down to search by city/state)
(Search by city/state or zip code - If you check the box for free, it will only list the free wi-fi spots. If you don't check the box, it will include pay wi-fi spots)
ALSO, I heard that there is a free program that you can download from Jiwire (a free Wi-Fi Internet finder), and it will even provide you with Wi-Fi locations while you aren't even online!