Without a car, should I stay as close to the town centre as possible?

My personal preference would always be the location that is easy walking distance from most of the sights. I like being able to come and go on my own schedule.

In these locals we always stay in town. From the hotels I pulled up in the area, you can some good ones in town.

Agree. The way I look at it, I'm spending a lot of money and effort to "be there". While I'm there, I want to be in the center, walking distance to attractions, and actually in the place I went to all the trouble to get to. I might be able to save a few bucks by staying further out and commuting in, but the most precious commodity is my time there in Europe. I want to make the best use of that, so I prefer staying in the old center, near all the things I came to see.

Yes. The “commuting” back and forth takes more time and mental energy than you think. You’ll be less likely to take a later night stroll or go out early when it’s peaceful. Stay as close in as you can. Countryside hotels are good but that’s for a different type of trip than you describe (farm experiences, bases for car-based day trips). Hotels just outside town when the town is your destination aren’t the best idea.

HOWEVER if you need to stay there, look at google maps street view for the route into town. 3KM isn’t very far. If the road seems safe for walking (sidewalks, lights and such) you really can walk it. In a city I might be staying in one neighborhood and easily walk 3KM to another without much thought. Of course that’s city streets, you’d need to see how your route is.

Also, taxis exist. If the savings is great enough it might be useful to consider.

I think the answer to this question is going to require some more research by you. The first thing on my list would be to contact the lodging and see not only how far the bus stop is located, but how often it stops. They may even have a schedule they can send you which would show how long it would take to get into and back from town from their location.
Have you downloaded the map and timetable sent you in your previous post and been able to figure out connections to the areas you want to visit.

In Ortisei, yes, stay in village. . We drove there and parked our car. We never used it during our stay. Look at Hitel Grones, on a hillside, walking distance to the elevator that takes you down to the village center, lifts, etc. This was one of our favorite hotel stays ever. When we booked , dinners were included and was fabulous.

Stay in city Centre. 3km might be on narrow lane, no lights, no sidewalk, much less no shoulder. Day like might be Ok, but night could be bad. Try google street view and “walk it online”.

I'm a public-transportation-only traveler, and the lodgings I've been disappointed in have been the ones that were just too far from the historic area of town, which was where I wanted to spend most of my time. Food might not be an issue at your proposed lodging in Ortisei, because I imagine that hotel offers half-board, so you could have dinner on-site if you wanted to. It may have quite a good restaurant. But in general I heartily dislike being in an area with no decent places to eat within 3 or 4 blocks. It makes me feel really isolated.

Thank you all for your advice.

We did as you suggested and chose a hotel in the town centre. We booked Garni Hotel Dr. Senoner.

I hope it's a goodie :)