Glass-bottom boats with thatched canopies ply shimmering lagoons. Tanned locals in pareus (sarongs) play ukuleles. Ridged velvet-green mountains punctuate the skyline. Palm trees reach higher than any roof. This is reality in the Cook Islands, a 15-isle archipelago marooned in the South Pacific. Go on a mountain safari on the main island of Rarotonga, or head to Aitutaki to stay in an overwater bungalow and motu-hop to deserted sugar beaches that beg to be Instagrammed.
You seem to have your heart set on Zakynthos but I have to say it’s not a good use of time for a sort-of overrated payoff. Your time is much better spent (in my opinion) seeing another Greek island in the cyclades (maybe taking a ferry to Naxos or Paros sitting outside on the deck drinking a bottle of wine) rather than taking a bus and connecting flights. Zakynthos and Santorini/Mykonos are on opposite sides of the country and the only way from one to the other is by flying (or some combination of bus and ferry). So, my recommendation is to consider spending those Zakynthos days in Naxos, Paros, Milos, or some other Cycladic island.
Argostoli is the capital on the mid-west flank of the island and is not really a destination itself, that moniker falling to the contiguous beach scene running from Lourdata south eastward to Skala. While development might have caught up here by now, it should still be a pleasant beach scene and focus for a relaxing stay. The Melissani Cave on the east coast is a must attraction and while it can be visited on a day excursion from anywhere on Kefallonia the two villages or Agia Efthymia and Poros are low-key ‘resorts’ pulling in a regular crowd of travellers and may warrant a look-in. The port of Pesada (just west of Lourdata) is the home of the local ferry to Zakynthos (Zante).
Since airline reservation requests are often made by city-pair (such as "show me flights from Chicago to Düsseldorf"), an airline that can codeshare with another airline for a variety of routes might be able to be listed as indeed offering a Chicago–Düsseldorf flight. The passenger is advised however, that airline no. 1 operates the flight from say Chicago to Amsterdam, and airline no. 2 operates the continuing flight (on a different airplane, sometimes from another terminal) to Düsseldorf. Thus the primary rationale for code sharing is to expand one's service offerings in city-pair terms to increase sales.