The CDC has an entire page about Breastfeeding. However, as is typical for US Government data projects, it doesn't get to a city level of granularity -- the CDC breast feeding data is aggregated at the state level.
You may be able to find comparable reports from some states -- for example, California publishes reports created as a part of their participation in the CDC's survey. I'm not optimistic that you'll find this for many other states, but we can improve this answer if you do! You might also be able to request the data using under FOIA/FOIL laws, even if it isn't published.
Another option would be to contact organizations like La Leche League, who promote breast feeding. A little bit of googling didn't turn up anything obvious, but they might be willing to share if they were approached.