ok, Vathi is the other town, or rather large village where the ferry stops, so cant advise much about places to eat as we only passed through there. Near Vathi, you have several beaches Fanari, Ambelaki, and Porto Elia which is the other side of the village of Katomeiri. There is only one road across the island. The one and only minibus meets the ferry at both ports - Spilia and Vathi, so if without a car as many people are, catch this to save your legs, it is quite an experience taking the minibus, adds to the fun of the holiday!!!.
To the south of Spartohori is another beach, well ....actually a strip of pebbles, very narrow, overlooking the Meganissi straight, here there is a good taverna for lunchtime, we walked this from Spartohori, about 40 mins, called Aghios Yiannis.
You can hire a boat for the day on Meganissi if that takes your fancy..any other trips you will need to get the early [7.45] ferry back to Nidri. Two I can recommend are the Odyssea, which takes you to the Submarine cave, back to Meganiisi! we stayed on the boat then, and a beach BBQ followed by Skorpios island and swimming off the Skorpios beach...the other was on the MS Christina, the Forgotten Islands ...takes you to 2 islands Kastos and Kalamos and they were stunning.
The car ferry comes over from Nidri about 5 times a day, not sure what September schedules are like though.
Have a great time...oh and when you return to Preveza airport, be patient, the queues are horrendous, but once checked in the taverna down the road is pretty good!
Oh, forgot to say, when driving through Katomeiri and Spartohori, the streets are extremly narrow, barely wide enough for a car, so if you meet something coming the other way, expect to have to back up or find a drive to dive down!