The first way to check is to turn on your wireless on your laptop and see what networks you have available. Most city-operated WiFi networks use an obviously named WiFi network name, so it should be easy for you to identify if there is one available. It will also give you an idea if you have neighbors with an unprotected wireless network (although you shouldn’t connect to those and leech their WiFi for free!)
There are also several websites you can go to and see if there is a municipal or city operated WiFi network, as many of the larger cities are covered with free WiFi. WiFinder is one and JIWire is another.
Note that depending on the wireless strength and how many people are using the service that it might not be quick enough to do things such as streaming television shows online, although watching YouTube videos should be fine (although you might have to wait for it to download first before viewing, which can be seen on the video you are viewing by the bar under the video). But if you are using it for email and random web surfing, it should be fine.
This also means that you can take your laptop along with you to the park or to your daughter’s dance practice, and get connected to the internet while you wait!
If you have a desktop computer, you can install an internal wireless connection or an external one with an antenna, and they can be purchased for fairly inexpensively now.