I would encourage you NOT to attempt sightseeing in Athens after an exhausting journey, arriving at 9 pm. Instead, I suggest you take a shuttle (it's free 24/7) 25 minutes to Hotel Avra, have a small snack and CRASH. Then the next AM you can shuttle BACK to Airport & catch an early flight to Santorini. Here are my experience-proved reasons for Athens last:
(1) With only 7 actual days, every hour is precious, and going into ATHens twice takes valuable time
(2) you'll be too exhausted for a sightseeing marathon in a busy city; instead, recover & re-energize on the islands
(3) this way you learn "how Greece works," thus can navigate Athens
(4) after even a few days of culture & ancient sites, famous Athens landmarks will resonate SO much more.
(5 this approach puts u in Santorini on the weekend, when there are fewest cruise & package-tour mobs
With this approach you could arrive Santorini 10 or 11 am on Day #2. I recommend staying Firostephani because of Ideal location; walkable to Fira town along cliffside path, but bypassed by tour groups. Also, do sunset dinner there or in FIra vs. OIA, due to those crowds. At 8 am Day #3 taxi or bus to OIA, have 2 hours to enjoy its views before the 10 am invasion of tour throngs. IF you are an archeology buff you could stay a day longer to explore Akrotiri etc, but if you are there mainly for the caldera view, why not check out and get the 3:15 ferry to Naxos on day 3 (Sept 5)? Stay in St. George beach, because u get a beach experience yet a 15 min walk to the port town attractions. You'd have an evening & 2 full days, and on Day 6 (Sept 8) fly Aegean to ATH on either a 9:50 or 10:35 flight. Only ONE trip into ATH (1 hr, flat-fare taxi €38) and 2.5 full days for sightseeing. Cruelly short visit, but the most efficient logistics, minimizing travel time ... only faster way to get around in the Aegean is a magic carpet & those are scarce lately.