With four days, as you said, not much time. You are really down to "What time do you arrive in Athens day 1?" and "What time do you leave out of Athens Day 4?"
Sure, you could book a flight Day 1 and get to Santorini, but in reality that day is shot travelling, maybe a nice evening, but little else. Day 2 you have in Santorini, but Day 3 you really need to be getting back to Athens, again shooting most of the day, leaving an evening in Athens before you fly out the next day. Probably no real time to see anything in Athens, other than what can be seen walking around. If Santorini is really what you want, then it works, just a bunch of traveling to get it. Santorini is one of the few islands that operate year round, but there will still be many places closed in early March. No need to do "Beach Time", maybe Akrotiri would be the main draw besides just seeing the Caldera.
Spending the time in Athens would allow more, see some things there, everything will be open. You might even do a day trip to Delphi or the Peloponnese. In the Peloponnese would be Mycenae, Epidaurus, and Corinth ancient sites, maybe do an overnight in Nafplio. Olympus might be too far.