The Tasman Bridge is part of the Tasman Highway (A3), which links Hobart to Launceston, and if you spend much time in Hobart, you'll likely both see and cross the Tasman Bridge. While it's not a tourist attraction on its own, there is a small lookout on the eastern side of the bridge. Hop-on, hop-off buses stop near the bridge, at the Royal Tasmanian Botanical Gardens.
The bridge is open to pedestrian and vehicular traffic, so you can walk or cycle across.
Bring layers and rain/sun protection if you plan to cross on foot, as the weather in Hobart can be unpredictable.
You can take in great views of the bridge from the Rosny Hill Lookout on the eastern side of the bridge.
The Tasman Bridge crosses the River Derwent, just north of the Central Business District. It's less than a 10-minute drive from the heart of the city, and lots of public buses—including lines 615, 624, 625, 634, and 646—cross the bridge. You can also rent a bike and ride over the bridge or take a bus or hop-on, hop-off service to the Royal Tasmanian Botanical Gardens and walk the rest of the way.
The Tasman Bridge is open 24 hours a day, 7 days a week. If you come during weekday morning or evening rush hours, you should expect a fair amount of traffic. The bridge is particularly pretty after dark, when it’s illuminated.
On the western side of the bridge in the Queens Domain area, the Royal Tasmanian Botanical Gardens is one of the oldest gardens of its kind in the country, dating back to 1818. The site encompasses around 35 acres (14 hectares) and features beautifully manicured walkways and a variety of gardens, including a herb garden and a traditional Japanese garden.