We stayed in Dobbiaco / Toblach. It was nice, much quieter than the more Italian bits. Not the same ski-lifts and stuff though – less of a resort place.
Also stopped briefly in Cortina, which is outrageously expensive, everything was fur coat shops and stuff, I wouldn’t recommend it unless you’re absolutely loaded and like being ripped off, we ended up heading further north after a couple of days. On the other hand, it is set up for mountain biking with the ski lifts and things.
There are first world war battlefields up in the high alps there which are incredible – worth a visit, and obviously they are on via-ferrata routes too.