We went on a hiking trip to the Dolomites a few years ago. The hikes were all spectacular, although many were quite challenging.

In the Tre Cime di Lavaredo area you can hike to several refugios, depending how long you want to hike. It doesn't take very long to get to the Rifugio Lavaredo - easy walking on a wide path. You can then continue on to the Rifugio Locatelli, or continue on around the entire Monte Paterno loop if you want an ambitious all day hike. I don't think any part of the loop was very difficult.

A beautiful, but challenging, hike in the same area is the Rifugio Fonda Savio Loop - you hike up too the Refugio Fonda Savio and then descend steeply into a valley with the aid of the fixed cables in the rock.This will give you a taste of the via ferrate, but not too overwhelming. If you don't want to do the steep descent you can just hike back on the well established trail you went up.

You might want to double check hotel availability in June - I seem to remember that most places close after the ski season and don't reopen until the end of June, beginning of July.

Leslie Chicago and Santa Fe