The best way to go online if you haven't got an Internet connection at home is to go to a nearby coffee shop. Yes, we know that some coffee shops have started to frown at people with their laptops, but in most coffee shops, this isn't a problem. Depending on where you live, part of your city might already be blanketed with free WiFi. While this isn't true for everyone, going to the local coffee shop is certainly an option. As you might have heard, Starbucks is no offering WiFi free for everyone, which is really nice when you are in an unfamiliar city.
There are also a bunch of different shops and libraries that offer free Internet. Libraries, at a university, college, or even a public library, usually have a bunch of different terminals to access the Internet. If your library had a recent overhaul, then you'll find new computers. Bookstores are also a good bet to find free Internet. Community centers are also a good idea.
All in all, I have to say that the Internet bill is the one bill that I don't mind paying. I don't have cable or satellite TV, but I do need high-speed Internet, preferably the fastest available.