If you don't have the means to leave Argostoli, you can go for a decent bath on Lassi beach. Lassi beach is just the regular beach with shallow water, lot of sunbeds and umbrellas, louder music and a fair amount of crowds.
This photos was taken from the road to Sami. It shows how well sheltered is the bay of Argostolion. (look at the map to better understand its situation). The city spreads over a cape, inside the bay. The very inner part of the bay (on the right) is like the arrow of a hook (foreground)
The main street is for pedestrians only and is lined by a great many shops. In the high season, it is not easy to park close to the city center and you might have to walk on a good distance. Somewhere around the southern entrance into the town should be a good choice.