If Atletico or Leipzig make the final, they will play on: August 13 - 18 - 23 (5 days between every match)
If PSG or Atalanta make the final, they will play on: August 12 - 18 - 23 (6 days between quarters and semi; 5 days between semis and finals). These two have the best schedule.
If Juve, Lyon, Real or City make the final, they will play on: August 7 - 15 - 19 - 23 (8 days between 1/8 and 1/4, then 4 days + 4 days)
If Napoli, Barca, Bayern or Chelsea make the final, they will play on: August 8 - 14 - 19 - 23 (6 days between 1/8 and 1/4, then 5+4 days)
So PSG and Atalanta have the best schedule, with no 1/8 finals, 6 days rest between quarters and semis and 5 days rest between semis and finals.
As for those who have it the worst... I think it's Juve/Lyon/City and Real. They will have 8 days rest between 1/8 and 1/4 finals, but after that they have only 4 days between quarters-semis and semis-final.