Nagasaki Biopark is a massive outdoor animal park - sort of a cross between a petting zoo with tame animals that you can feed and a regular zoo with less domesticated animals. There are around 2000 animals from 200 species spread out over 30 hectares, so there's plenty of animal interaction to fill a two- or three-hour visit. While you're here you can also drop in to the PAW animal cafe at the park entrance, where you can enjoy the company of dogs and cats, rabbits and guinea pigs.
If you don't want to go by car, there are three shuttle buses a day in each direction from the entrance to Huis Ten Bosch amusement park (next to JR Huis Ten Bosch station). The trip takes 45 minutes each way and runs along a very scenic route. Online bus reservations are required, and three hours is probably a good amount of time to plan for your visit, factoring in time for lunch-eating, dog-petting and gift-store shopping. Note that some of the animals go off duty about thirty minutes before the park's official closing time.
A herd of friendly capybaras is one of the main attractions here, and there are instructions on the website explaining how to pet them. You can also feed the llamas, Patagonian maras, goats, sheep and several other tame animals, and you can sign up to hand-feed the Brazilian tapir and the hippopotamuses at set times (on weekends only), for a small additional fee. In the winter (December through February) you can watch capybaras enjoying their own hot spring, and in the summer whole watermelons are fed to the five resident hippos twice a day.
In addition to the various animal enclosures there's a big tropical greenhouse with a butterfly garden, plus a separate insect museum. A few different cafes and dining spots serve casual Japanese fare throughout the day. We enjoyed a very tasty pork cutlet roll for lunch, a local Nagasaki specialty.
You can get a combination ticket for the Biopark and a one-hour visit to PAW animal cafe, and you can extend your PAW visit for Y500 for each additional hour. Unlike most other animal cafes PAW doesn't actually serve coffee, but there are coffee and ice-cream stands at the entrance to Biopark, alongside a well-stocked gift store.