My favorite place is the Brenta Dolomites, I have hiked almost all the classic Via Ferratas there several times since 1999. I heartily recommend that every body with reasonable head for heights and not too much of a beer belly go there at least once. Best starting point is Madonna di Campiglio, cable car up to the mountains and then 1-7 days just hiking and climbing from refugio to refugio, no need to come down in between. Possible months for this are July-September. Costs about 65-80€ day with half board in the refugios, lunch and occasional beer/glass of vine/grappa.