I would look at Dachstein, which is about a 10 minute drive from Hallstatt. You can take a cable car to the first level and do the ice caves [to get up there, it's a 15-20 minute hike by itself]. Even if you don't do the caves, the area right around there is beautiful. You can also go up to the second level to hike out to the various view points. The third level has more intensive hikes but nothing says you can't wander half a mile and then go back.
With a three year old, wandering around up top around the funicular in Hallstatt and walking out to the little viewpoint would also be easy and nice. The cafe offers a world class view on a nice day.
As for eating, I'll say Hallstatt offers... fine? ... restaurants. We ate in the Heritage Hotel's restaurant and the See Hotel Gruner Baum's restaurant for dinner. They were both fine with the later being the better off the two. Nothing was spectacular but I enjoyed my fresh fish. Hallstatt kinda shuts down at night so any of the hotel restaurants are going to be your best bet. There was a little hot dog stand across from the Heritage Hotel that was good in a pinch. Otherwise it's all pretty standard touristy fare.
As for breakfasts, majority of the hotels offer the standard Austrian continental, which you can pay for as a non-guest. I had no complaints about any of the 5 hotels we stayed at across Germany/Austria in late July in terms of their breakfasts. Fruits, meats, breads, veggies, ect.
