Leavenworth is a Bavarian-style town. Oktober Fest happens every weekend in October so there will be plenty to do downtown. There is also a park by the Icicle River that is nice for a scenic walk. Grab a pretzel and yodel around the streets - you'll fit right in.
You might need to plan early for this one - this trailhead now requires a permit. But if you have the time and energy to get to Colchuck Lake, you will not be disappointed.
If you have some time during your visit, definitely take the opportunity to hit up a winery. Leavenworth is surrounded by them and it's easy to find one with beautiful views. Head towards Peshastin or Cashmere to find a quieter location.