Originally Posted by KLouis

There is, to my knowledge, no domestic flight into/from Corfu, other than Athens. That excludes a stopover flying to the island. Also, ferries connect Corfu with Igoumenitsa, Paxoi and Patras. Igoumenitsa and Patras (the former is 1 hour away, the latter between 6-8), but neither is worth a stay for more than 1 hour (waiting to board), and there is no flight from either from/to ATH. Paxoi is a very nice small island, nothing to see but great for relaxation, but it is also only 1.5 hours away by boat. The only solution is that you book from wherever to/from Athens and then you get a rental. Plenty of places to visit on the way (e.g. Meteora, already suggested, a big detour but really worth it), Delphi (smaller detour, also worth it), as well as nice beach-front villages such as Parga or other nice towns (e.g. Lefkas, Preveza). Depending on what your mood/taste, inland places such as Zagori are also amazing. But, as I said, you'll need a car!

PS They used to have a ferry boat connecting all Ionian islands twice a week with Patras but I think they stopped that last year (lack of enough tourists). That would be ideal for your purpose but I doubt that it will run again this year, especially after the Covid-19 situation...