Monguelfo, Villabassa, Dobbiaco are good bases for Braies. - From Dobbiaco the drive to Misurina and the main road access to Tre cime is about half an hour, from Villabassa or Monguelfo marginally longer, so any of these three villages is a good base for both sights. Actually the drive from Dobbiaco to Misurina is easier than the drive from Cortina to Misurina.
Tre Cime can also be accessed from the back, through Sesto and Val Fiscalina. But the walk up from the Val Fiscalina parking to Rifugio Locatelli is 3 hours long ascending, with a 1000 meters difference in height, so is appropriate only to very fit and well equipped hikers on a good weather day, but incredibily scenic.