For the MLB's AAA leagues, I'd think the International League would have carried on, and the American Association would have joined with them. So I combined them into the Atlantic Coast Association.
These teams mostly use existing logos/unis, but I've grabbed a few out of the SFGiants58 conversion threads, and I'll link those here:
International League North
Lehigh Valley Iron Pigs (PHI)
Rochester Red Wings (WAS)
Scranton WB Rail Riders (NYY)
Buffalo Bisons (TOR)
Syracuse Chiefs (BKN)
IL South
Miami Marlins (BOS)
Charlotte Knights (CHW)
Norfolk Tides (BAL)
Atlanta Firebirds (MIL)
San Juan Expos (MON)
American Association North
Columbus Clippers (CLE)
Indianapolis Arrows (PIT)
Toledo Mud Hens (DET)
Iowa Cubs (CHC)
St. Paul Saints (MIN)
AA South
Nashville Sounds (DAL)
Louisville Bats (CIN)
Memphis Redbirds (STL)
Omaha Storm Chasers (KC)
New Orleans Zephyrs (HOU)