Dolomites (Dobbiaco) suggestions

This might be helpful. There are several other related posts if you search in the forum.
https://community.ricksteves.com/travel-forum/italy/dobbachio

I can't help with Dobbiaco but we stayed five nights in Ortisei last summer in an apartment. I will agree with those who say the restaurants in town are nothing special. But we had lunches every day in the Refugios and that was special. For dinner, we had take out pizza or calazone or I made simple meals of pasta and salad. We ate out once and it wasn't as good as other places in Italy quite honestly.

Still, I would stay in an apartment again as we like more space and frankly cooking a simple dinner after hiking was easier than going out to eat. There is a grocery store very central that we went to almost every day.

I do not think that the half board hotel is a necessary experience. The correct way to put it is that if you stay in an hotel, taking the half board dinner is more practical and cheaper that finding a restaurant every evening. And South Tyrol restaurant are a bit on the expensive side. But the half board dinner is not always the world's eighth wonder; if any, the hotel breakfast buffet is often the most memorable meal.
Another thing to consider is that if you are staying 4 nights in a place, maybe an hotel is easier than an apartment. I prefer apartments as I can cook on my own, but I am talking about longer stays (10 to 20 days); for 4 days I would prefer an hotel.
If you want to cook on your own in your apartment, Dobbiaco has only tiny supermarkets but has a big latteria (dairy shop) with a deli section and a large selection of local cheeses.
I admit that the hikes from Ortisei are the top ones and Dobbiaco is not as good on this side, but it much less trafficked and has the big advantage of being on a railway line, a rarity in the Dolomites. If you have a car, you have access to several nice places with a short drive from Dobbiaco.

Are you going to see Tre Cime? This is a must. Be sure to check the weather beforehand.

I have stayed at, and highly recommend, an apartment at Villa Glauber. It's a 5-minute walk to the centre of town but has hiking/skiing trails right out the door. It was a great experience and I would happily go back.