I have absolutely no clue how to find a relevant database.
There are three ways you could go:
1. Find an existing data source. Sometimes you can use data that other people/companies make available, either for free or by licensing it. The government is a great source for some kinds of data -- various agencies like the National Weather Service, NOAA, USGS, and many others provide lots of free and easily accessible information. I'm not aware of a National Pizza Price Registry, so the government probably won't help much in your example. You might need to look for a proprietary database that you can license.
2. Develop your own data source. I'm sure there are quite a few pizza joints in Chicago, and calling them all up periodically to gather their prices will be a lot of work. Many of those places will have web sites, though, so maybe you can automate part of that data collection, and the work to fill in the holes may be worth the effort to you.
3. Get other people to build your database for you. Crowd sourcing data to improve your database is a popular way to go, especially among small developers, because it lets you cover lots of ground at zero cost to you. It works best for sites like Twitter, Facebook, and StackOverflow where the data is naturally provided by the users. But it can also work for gathering other kinds of data, especially if helping to update the data has some benefit to the users. For example, your pizza app might let users review their pie consuming experiences, and your review submission process might include questions like 'what kind of pizza did you order?' and 'how much did your pizza cost?'. Users get to express their opinions, and you get the pizza price data you're looking for.