I am here to help, so feel free to reach out and I can help plan your itinerary.
If you are going all the way to Greece, I would recommend at least two nights in Athens either on the way over or the way back. The sites there are amazing and the Acropolis is one of the top ten man-made wonders of the world. Santorini requires at least three days, but I recommend four since there is so much to do and see. If you are only planning a week, then you have time for Athens and Santorini. If you can extend it to ten days (or more) then you have time for one additional island. Another option for longer trips is a stopover in a connecting city on the way over or back. Some options for common stopovers include; London, Dublin, Zurich, Amsterdam, Munich, Lisbon and Paris.
If you want to skip Athens, there are direct flights to Santorini from Barcelona, Rome, London, Dublin, and Zurich. One option would be to go to Dublin, spend a few days and then take a flight directly to Santorini. There are also direct flights to Dublin from Hartford. This leaves many options.
What I have learned is that it is still more cost-effective to buy a round trip than two one-way tickets. To save money you will have to pick a base city, like Athens (or another), and then buy one-way tickets. Then you can buy island tickets for Santorini. The best prices for airfare to Europe is around 6 months before your departure. Inner Europe flights can be bought much later if you want, the prices are always low.
Here is an example of what you can do:
1) Fly into Athens and spend a few days there. Don’t forget that you typically lose a day flying, if you leave in the afternoon, you will arrive in Athens the next morning.
2) Get a flight to Santorini from Athens. I prefer Olympic Air since they have so many flights and don’t nickel and dime you a lot (as of this writing).
3) Take a ferry from Santorini to Paros, Naxos, or Mykonos. Use https://www.ferryhopper.com to see rates and schedules. Ferries are really easy in Greece. You show us 30 minutes before departure and get in line to board the ferry. They are also really nice, like cruise ships vs the ferries we are used to in CT and Rhode Island. They have several restaurants and bars on board.
4) Take a plane back to Athens and spend the night at a resort in Vravrona which is 10 minutes from the airport. I recommend staying at the Dolce Wyndham in Vravrona (https://www.wyndhamhotels.com/dolce/vravrona-greece/dolce-athens-attica-riviera/overview), the property is gorgeous, and has a fantastic breakfast. They also offer airport transportation. Just be sure to use Booking.com vs making reservations directly since their prices are 1/2 the advertised rate.
5) Fly home the next day to the US. Note that you will get back the same day only hours after you leave thanks to the time difference.