Zoos have begun staffing up for the summer internship season. Most internships are unpaid and with no housing. There are some exceptions but you have to search for them. Your college may have stipends available for students interning at non profits.
Also check for paid jobs at each zoo. There are occasionally student worker jobs such as supervising the butterfly houses or in the summer day camps.
Zookeeper internships involve a lot of food prep, cleaning of enclosures, cleaning behind the scenes, operant conditioning (example: training for behaviors in order to check for physical health), record keeping, enrichment planning, and interactions with the public.
Each zoo will have different policies as to how many days and week or hours you will be working. Some are 8 hours a day with some weekends. Some will rotate days on and off. Most start pretty early in the morning.
The business side of zoos also take interns for event planning, foundation fundraising, marketing and social media.
The Association of Zoos and Aquariums accredits places that meet stringent requirements for health, safety, and financial practices. They are not your small roadside shows with sad and neglected animals.
Internships are posted on the AZA job board: https://www.aza.org/jobs. However, this list is constantly changing and evolving.
I will post links to some zoos and their internship links so that you can compare internships and plan for what kinds of materials and references you will generally need.
John Ball Zoo, Michigan http://www.jbzoo.org/support/internship a college nearby has housing for rent http://www.gvsu.edu/internhousing/
Minnesota Zoo, Minnesota http://mnzoo.org/internships/
Como Park Zoo, Minnesota http://www.comozooconservatory.org/support/volunteer/internships/#/internships
Columbus Zoo, Ohio https://www.columbuszoo.org/home/about/internships
Blank Park Zoo, Iowa https://www.blankparkzoo.com/contact-us/jobs/
Milwaukee zoo, Wisconsin http://www.zoosociety.org/About/Employment.php
Franklin Park Zoo, Stone Zoo, Boston area http://www.zoonewengland.org/jobs-volunteering
Omaha Zoo, Nebraska http://www.omahazoo.com/education/volunteer/job-shadowing/ I think there may be some housing if you plan way ahead?
Cincinnati Zoo http://cincinnatizoo.org/about-us/job-opportunities/
Lake Superior Zoo, Minnesota http://www.lszooduluth.org/about-the-zoo/employment/internships/
Great Lakes Aquarium, Minnesota http://glaquarium.org/about-us/jobs-and-internships/
Lowry Park Zoo, Florida http://www.lowryparkzoo.org/about/career
Red River Zoo, North Dakota http://redriverzoo.org/zookeeping-internships/
Shedd Aquarium, Chicago http://www.sheddaquarium.org/About-Us/Jobs-Internships-and-Volunteering/Internships/
Binder Park Zoo, Michigan http://www.binderparkzoo.org/employment/index.php#internships
Alaska Sealife Center, Seward Alaska http://www.alaskasealife.org/summer_fellowships Housing provided
Little Rock Zoo, Arkansas http://www.littlerockzoo.com/animalcareinternships
Bermuda Aquarium takes 1 US student per year. Housing, food and public transportation pass http://www.atlanticconservationpartnership.com/learning-experiences/internship-program-college-students
The Wilds in Ohio has onsite housing for rent https://thewilds.columbuszoo.org/home/about/join-our-team/internships/the-wilds-animal-management-apprenticeship and https://thewilds.columbuszoo.org/home/about/join-our-team/internships/the-wilds-animal-management-apprenticeship
Georgia Aquarium has a huge number and variety of internships http://www.georgiaaquarium.org/experience/support/get-involved/internships