Where can I bring my ESA:

ESAs are only protected by the Fair Housing Act and the Air Carrier Access Act (and loosely the EEOC). Which means they aren't covered by a Public Access Right and can't be taken to places such as stores, restaurants, clinics, etc. ESAs are not considered Service Animals and so are not covered under the same umbrella laws. This is due to the fact that ESAs are not required to have professional training (unlike Service Animals). Legally, it's up to the individual establishment on whether they allow ESAs. So it's best to call ahead and ask an establishment if you are allowed to bring your ESA before making the trip. Even after you arrive, the establishment is still allowed to ask you to leave without cause.

For more information regarding this subject, check out When is it okay to reject an ESA from an establishment and What laws protect ESAs