Parga looks like an Ionian island town and it is on the mainland, on the coast of Epirus opposite Paxos. There is no ferry from Athens because none is needed, and that is the single most useful thing to know before planning.
Diagram by Greece Trips. Free to reuse with credit - CC BY 4.0.
By road
The main way. From Athens the route runs west and then north up the Ionian coast, on motorway for a good part of it and on ordinary road for the rest.
We print no drive times. They depend on the traffic leaving Athens, the season and your own pace, and a printed figure is the fastest thing on a travel page to go wrong. Driving in Greece covers the road rules and the tolls.
The advantage of arriving by car is the one Parga shares with Lefkada: nothing about your trip depends on a sailing, and the Epirus coast either side is worth having wheels for.
By air
Two airports serve this corner. Preveza, to the south, is the nearer and is the one most visitors use, with a short drive north up the coast. Ioannina, inland over the mountains, is the other, and the drive from there crosses the Pindus, which is spectacular and slower.
Preveza also serves Lefkada, which is why a fly-drive taking in both is a common shape for this coast.
By bus, and the thing nobody tells you
The intercity bus network reaches Parga, usually with a change. The durable fact worth carrying is that the KTEL network publishes no single national timetable: each regional operator publishes its own, and connections between them are not designed to meet.
That is why bus travel across Greece needs checking region by region rather than looked up once. It is workable and it is not something to plan a tight connection around.
Once you are there
Parga is a base rather than an endpoint. Boats run across to Paxos and Antipaxos in season, the Acheron springs are a short drive inland, and Sivota up the coast has a scatter of islets offshore.
Day trips from Parga covers what is reachable, and the Parga itinerary covers the town itself.
Where this leaves you
No ferry, because none exists and none is needed. Drive west from Athens, or fly into Preveza and drive north for a short way. Take a car either way: the Epirus coast rewards it and the day trips from Parga are all either a boat you take from the town or a drive you make yourself. If you are relying on buses, check each regional operator separately, because there is no national timetable to check.
Quick answers
Is there a ferry from Athens to Parga?
No. Parga is on the mainland coast of Epirus, so it is reached by road. It looks like an Ionian island town because it was Venetian and then briefly British and was administered with the islands, but no crossing is involved.
What is the nearest airport to Parga?
Preveza, to the south, with a short drive north up the coast. Ioannina inland is the alternative and the drive from there crosses the Pindus mountains. Preveza also serves Lefkada, which makes a combined fly-drive easy.
Can you get to Parga by bus from Athens?
Yes, usually with a change. Be aware that the KTEL intercity network publishes no single national timetable: each regional operator publishes its own and the connections are not designed to meet, so check each leg separately.
Do you need a car in Parga?
The town itself is walkable, but the reasons to base there mostly need one: the Acheron springs inland, the coast towards Sivota, and the drive up to Ioannina. The boat to Paxos is the exception.