Well done.
In Lassi behind Argostoli the long and wide glass. Nice waters but it gets crowded.
In Lourdata as you go from Argostoli to Poros. Large beach, quiet but with very fine sand.
In general, all the southern beaches are like this, but there it is thin. One of the same is in Skala.
If you go that way, Katelios has good fish restaurants.
1) Antisamos, nice green beach with pebbles. It is more beautiful for morning-lunch bathing as seen by the sun. After that you go to Agia Efimia to eat in the small taverns that it has on a hill above the sea.
2) Petani, it reminds a bit of Myrtle but nicer in my opinion. I liked Myrtos only from above.
3) Definitely a visit to Assos
4) From the Lixouri side, go to Xi and Vatsa to the Tavern of the Crazy which is on the sand.
5) Palia Plaka at the port in Argostoli has good food and stews.
Go for a walk to the lighthouse of Argostoli in the afternoon when the sun goes down if you are the romantic type
6) Visit to the lake of Melissani at 12 noon when the sun is above the cave hole.
What you said, I think all the money is on the island. Right choice of accommodation because it has a lot of life and definitely the most "central" point for the excursions in which you should arm yourself with patience because the distances are huge and at the same time with a lot of attention because the roads were (I don't know how they are) miserable
Petani, Xi, Antisamos, Myrtos the best beaches. The last one, although more famous, you have to hope to reach it without a wave and find a place to park. The 2 Glasses (Long-Wide), quite good (if I remember one I liked more) with enough people and beach bars
Assos is by far the most picturesque village, Fiskardo the nicest for hanging out and eating in the afternoon. Agia Efimia also very nice family with many options for food. I liked evening.
As for Melissani and Ag. Gerasimos is worth a visit...
ALEX will tell you about more popular places.
My advice if you want to see the island is to divide the map into 4 parts (NW, NE, SW, SE) because otherwise the kilometers will eat you up.