Started our hike at the Tre Cime, but felt like 30 euros for a touristic walk around Tre Cime just wasn't worth it. Hired Via Ferrata gear, and took the via ferrata up to the top of Monte Paterno. Highly recommended if you're not afraid of heights. The via ferrata itself is not too difficult either. Most people start from Forcella Lavaredo; we went to Rifugio Locatelli, then turned back to go up to Mt Paterno. Not sure which is the best option, I liked ours very much. Make sure to bring a headilght for the short part in the tunnels (not claustrophobic at all, no worries) near Rifugio Locatelli.

Lots of vertical in this via Ferrata. Short hike from parking is also a plus. Run out and the traverses at the end are not for the faint of heart. One or two, is you fall, you die spots. Saw a women carrying her dog over one such crux. Europe. Then a great hike out to he Laghindi Lavaredo hut.