Can I take my ESA to public places?

Unfortunately, emotional support animals are not treated the same as service animals. Public establishments do not fall under the Fair Housing Act or Air Carrier Access Act which are the laws that protect ESA's in housing and for flying domestically. Public establishments are not required by law to accept ESA's but to my knowledge, some places that will. You can reach out to the establishment to confirm that they are pet-friendly.

https://www.certapet.com/emotional-support-animal-laws/

https://www.animallaw.info/article/faqs-emotional-support-animals

http://servicedogcentral.org/content/ESA-flying

https://adata.org/publication/service-animals-booklet