We are considering staying in Sterzing/Vipiteno next summer. How many days is best for the South Tyrol? We can probably spend up to six days. We won't have a car.

Thank you.

It's up to you to decide what's best for you. Some people just spend 1 night in a Alto Adige town between 2 trains, others stay there 3 or 4 weeks.
The city of Sterzing only can be visited within 1-2 hrs.

There is a direct correlation between what you can see/do and the time required when using public transportation. So, what do you want to do in the area and have you investigated the public trans options from Vipiteno?

We enjoy walking and the outdoors in particular. Old towns and castles appeal as well.

We are interested in seeing the lakes and waterfalls, and places like Trauttmansdorff Castle Gardens, Merano and Bolzano.

We usually stay in small to medium sized towns and use them as bases. I know Sterzing is not very big but we can use it as a base for exploring the region by train and bus. It seems that we will get free transport with the activeCARD in Sterzing.

Earlier this year we did something similar, staying in Meersburg on Lake Constance and did day trips from there.

Sterzing may be a good base for the waterfalls of Ratschings, Pisciadu and Sand in Taufers. For all other things you mention, Bozen would be better.
The old city of Bozen with it's loggias is very scenic and you will not feel like in a big town there.