Unless perhaps you live in a rural area. I've been using the Chicago Board of Elections website , for years. There (see http://www.chicagoelections.com/en/home.html and http://www.chicagoelections.com/en/your-voter-information.html ) you see not just your polling place, but much more:
Verify your voter registration
Locate your polling place
Obtain a sample ballot
Find contact information for your public officials
Check the status of your absentee ballot
Apply online for an absentee ballot
You don't register to vote with the state, but rather with your municipality. It's important not just to be registered and to be sure of your polling place (mine changed this past year), but to be able to study the sample ballot for upcoming races for your city, state, and federal offices (these will all be different, depending on where you live, with lots of local offices and judgeships, and different US Representatives, even).
For every primary and election, I print up a sample ballot and do lots of research, and then bring my "cheat sheet" ballot to the poll. I can also check election returns on the same site, after I've voted.
It's a good service from the state, but it's not complete enough to help inform voters fully.