There really aren't big travel cost savings moving to the Big East.
Go sport by sport and UConn may reduce about 10 longer trips per year for non-revenue sports (still will have trips, but not as far) and maybe 8 to 10 long trips combined for men's and women's basketball (still have to travel to Milwaukee, Chicago, Wichita, Ohio, Indiana). Based on rumored schedules, there doesn't appear to be reduced travel for football.
Many people don't understand that some of the non-revenue sports have 1 AAC event per year:
Golf (no change in travel as Big East conference tournament is in the south as well.)
Swimming and Diving
Track and Field
Women's Rowing
And, some sports were already not playing in the AAC:
Men's hockey
Women's hockey
Field Hockey
Bottom line is that the move to the Big East was to improve the basketball situation at UConn and to perhaps generate more media revenues than the crappy AAC media deal. If we can improve basketball season ticket sales and donations by moving to the Big East, that's a bonus.