Sunday

10) 10 a.m. Walsh’s world

The Museum of Old and New Art (entry 30 Australian Dollars), founded by David Walsh, an art collector who built a fortune from gambling, has become much more than an art institution. It’s spawned two popular (and more than a little subversive) art and music festivals — MOFO and Dark MOFO — in addition to art-filled luxury pavilion accommodations (from 750 Australian dollars a night) and, coming soon, a 172-room hotel (as yet unnamed after several controversial choices). The museum itself is a lot to take in, so arrive early and plan to get lost in the cavernous space showcasing Mr. Walsh’s outlandish collection. Be sure to check out the four fantastically disorienting James Turrell light installations commissioned for the new Pharos wing (separate tickets and advance booking, 10 to 25 Australian dollars), as well as the newly opened underground network of tunnels and chambers filled with works by Ai Weiwei and Alfredo Jaar. On a pleasant day, take a break on the lawn with a glass of Moorilla sparkling Riesling (10 Australian dollars) or a Moo Brew Pilsner (9 Australian dollars) — Mr. Walsh owns the winery and brewery, too. A fast ferry offers 25-minute connections to the museum from downtown Hobart (from 22 Australian dollars roundtrip).

11) 2 p.m. Farm to former asylum

Long before Tasmania became a foodie destination, Rodney Dunn and Severine Demanet ditched city life to set up a farm and cooking school in the Tasmanian countryside. Nearly a decade later, the couple completed the farm-to-table circle with the opening of The Agrarian Kitchen Eatery in a rather unlikely location: a sprawling asylum in the town of New Norfolk (about 20 miles from Hobart), which operated for over 170 years before closing in 2000. A tour of the grounds reveals glimpses of the institution’s notorious history, but inside, the focus is on the seasonal menu, which highlights ingredients from the farm and other local producers: sugarloaf cabbage with lovage seed mayonnaise and preserved fish (23 Australian dollars) and slow-roasted Derwent Valley lamb (a sharing dish for 140 Australian dollars). It’s a glimpse of the present-day potential of the island, risen from a painful past.

Lodging

Hobart is an extremely walkable city if you base yourself centrally near the wharf on the River Derwent. Check out the Battery Point neighborhood, which is accessible to Salamanca Place via the 19th-century Kelly’s Steps; apartments here on Airbnb rent for 200 to 250 Australian dollars per night.

From the Dutch explorer Abel Tasman (the first European to land on Tasmania) to the cricket hero Ricky Ponting, each of the 114 rooms at the new MACq 01 Hotel is devoted to a different character in Tasmanian history, with illustrations on the door and their full stories and other artifacts featured prominently inside. Doubles from 240 Australian dollars.

The nearly 150-year-old Lenna of Hobart was once the mansion of a wealthy Tasmanian whaling merchant, Alexander McGregor, who oversaw the largest individually owned fleet of ships in the Southern Hemisphere. Doubles from 208 Australian dollars.