If you're looking to stay away from TDY's, don't even think about tankers (KC-10, KC-135). Before 9-11, most crewmembers in my squadron were TDY an average of 120+days/year, but since then, an average of 200+days/year. These were not fun trips either, mostly long deployments in tents in the Mid-east.
The only "TDY havens" that I know of are OSA (Operational Support Aircraft) assignments (C-21's), and stateside helicopter assignments (UH-1). You may be good enough to get a FAIP (First Assignment Instructor Pilot) slot at UPT, but nothing's guaranteed.
Before you go all the way with this active duty thing, go talk to your in-service recruiter and a local AFRES/ANG flying unit about pilot opportunities. Active Duty "E" to Reserve pilot "O" is a very good deal, it may be a better option for you.
From experience - Bottom line "Stay away from (Active-duty) tankers!"