Freycinet National Park
Freycinet National Park is on the East Coast of Tasmania. It is one of Tasmania's first National Parks, being established in 1916. There are several very nice beaches there, including the famous Wineglass Bay.
Freycinet National Park is administered by the Parks and Wildlife Service of Tasmania. http://www.parks.tas.gov.au/natparks/freycinet/
Freycinet National Park was named after its founder, Louis de Freycinet.
Flora and fauna
It's about two and a half hours drive from Hobart.
You need a permit for all of Tasmania's National Parks. They can be bought at the national park visitor centre at the park entrance, and there are several different options from a day pass for just this one national park to a pass that is valid for an entire year and includes all National Parks of Tasmania.
The fees are shown below (currency is in Australian dollar):
Daily Pass: Per vehicle (up to 8 people): $20 Per person: $10
Please note that you have to pay for per person and for a vehicle. For example, if a family of four wants to enter with one car, they will have to pay $20 for the vehicle, and $40 for four people, in total $60.