The Dolomites are not only beautiful, there is access to incredible mountain scenery and activity for even the least fit people, all without a car. You can hike for 30 minutes or all day. You take cablecars to high mountain meadows, walk to a rifugio where you can have refreshments from a perfect espresso to a full hot meal and find a clean restroom. You will walk through pastureland with horses and cows grazing, and at high altitudes may spot a marmot. We have been hiking now for three weeks and have yet to run out of possibilities.
The little Tyrolean towns are charming. We particularly like Ortisei in the Val Gardena. Lots of shops, community activities, highly strollable, and peaceful.
You can get here without a car. Train to Bolzano then bus or private transfer to Ortisei. (Euro 85 for the transfer but with baby and equipment it might be worthwhile.) Once here, the buses are free with a pass issued by your lodging. You can reach many destinations on the bus network, or you can buy a lift pass to access the high areas. There is a lot of info at the Val Gardena website.
Also, the Alpe di Siusi is a possible place to stay so you get the high mountain meadow experience overnight. We did a combo a couple of years ago with two nights in the Alpe di Siusi and four in the valley in Ortisei. Gave us a nice range of experiences. You might look at the Hotel Saltria in the Alpe di Siusi.
In Ortisei there are tons of lodging possibilities from simple B&Bs to grand hotels catering to families. I will PM you as well.
