Most of the sites to visit in Athens are concentrated in the same area which is easily doable by walking (the entire area around the Acropolis is pedestrian).
See this map:
https://www.google.com/maps/d/edit?mid=1OhGNGU1LUEgwFTul8u4YEe_tijF8Hqs&usp=sharing
Also note that the "Hop on - Hop off" buses will only take you around the main avenues of Athens and you will not see much other than road traffic.
A few days before your stay in Athens you can buy tickets to visit the main sites on the official website:
https://hhticket.gr/tap_b2c_new/english/tap.exe?PM=P1N
There is a new reservation system which is gradually being put into service and which may impose a time slot for visiting the Acropolis.
Nothing has been officially specified yet.
That being said, in May you shouldn't have too many problems with crowds and queues.
From May to October A bus (X80) runs between the cruise terminals and the center of Athens, see details here:
https://www.oasa.gr/en/visit-athens/x80-piraeus-acropolis-syntagma-express-bus-line/
The flat rate for an Athens center → Airport taxi journey is currently €40 from 5:00 a.m. to Midnight (tolls and luggage included)
If you ask hotel staff to book a taxi for you, they may charge you extra.
Or you can book it yourself with for example:
https://www.welcomepickups.com/athens/
Allow between 45 minutes and 1 hour to go from the center of Athens to the airport by taxi