I've cruised out of Athens pre-Covid on a B2B, returned to US from Barcelona. Flights were DFW to Athens w/layover in Philly; return Barcelona to DFW w/layover in Chicago. To avoid claiming & rechecking luggage, highly recommend non-stop flights; if that's not possible, try to have your layovers in a US city. Due to airport delay, we missed our connection in Chicago and had to stay overnight. I would much prefer being delayed in a US location than foreign city where I may not speak the language or know how to navigate (please, no lectures); I'm too old for unplanned deviations.
Due to my phobia, we didn't stay in a hotel pre or post cruise and used the ship (Princess) airport transfer so I can't comment on hotels, taxis, Uber, etc.
I remember customs and check in being straightforward but lengthy (it is international). I really think the ridiculously long process in Vancouver BC is worse than what we experienced in Athens.
Turnaround day was in Athens. Since we weren't adding any land time but wanting to see what we could of Athens, we got off the ship with the first group and onto a Hop On Hop Off that we were able to pick up in the parking lot. We returned very close to All Aboard, had our In Transit cards & Passports - easy peasy.
At the end of the cruise, we disembarked in Barcelona. We did an excursion w/airport transfer through the ship to allow us to see some of Barcelona and not worry about/hassle with luggage. It was flawless.
I had minimal non-cruise international travel experience (So Africa, Mexico, Canada) and my travel companion had none. She got Global Entry specifically for the cruise flights - it did allow her to move through the airports quicker and gave her peace of mind that was well worth the $100 cost. I have TSA Precheck, but that doesn't help internationally - I was a bit envious and recommend getting Global Entry if you can. We did not have any issues, had ample time to get from the airport to ship and enjoyed the Hop On Hop Off in Athens.
Although we don't do it for US (or Vancouver) cruises, we did book flights through the cruiseline.
Take adapters in your carry-on so you can charge your phone at the airport (and hotel if you stay over).
Interested in reading others thoughts - I'm sure you'll get some good tips.