The High Country Rail Trail passes straight through Tallangatta and is the town's best reason to stop. The 8 km ride to Old Tallangatta Lookout is the easy classic: mostly flat, family-friendly, and close to the Lake Hume shore.
If you have more time, continue west toward Wodonga for long water views, or east into quieter country where the old railway begins to climb. Bring your own bike; Tallangatta is useful as a trail stop but does not have the depth of services of Bright or Wodonga.