For Cortina, Venice wins because the public-transport chain is unusually clean by Dolomites standards. Cortina Express runs several daily buses between Venice Airport and Cortina in summer, with the airport departure at 07:00, 11:20, 14:20, 17:20 and 19:00 and arrival in Cortina at 09:30, 13:30, 16:30, 19:30 and 21:30 on the current timetable. Treviso uses the same corridor and is slightly shorter on the road.
For Val Gardena the geometry flips north. The official Val Gardena access page lists Innsbruck at 190 km, Verona at 190 km, Venice at 250 km, Treviso at 260 km, Bergamo at 280 km and Munich at 320 km. In practice Innsbruck usually feels easiest because the transfer chain is simple: airport to Innsbruck Hbf, train south to Bolzano, then bus or transfer into the valley.
For Val di Fassa the official valley page lists Bolzano Airport at 40 km, Treviso at 160 km, Venice at 175 km, Verona at 180 km, Bergamo at 280 km and Milan at 350 km. Bolzano is geographically closest but too small to plan around for most international visitors, so the practical shortlist is Verona, Venice, Treviso and Innsbruck.