I am planning a trip in May and will fly in to Athens. While we'll spend most of the later part of the trip in Skiathos Greece, I'd like to plan a weeklong trip to Italy by public transportation. I've checked the southern bus,train,ferry route to the Brindisi and also the northern train route to Venice. Is there a recommendation or which would be better? Traveling with a first time-to-Italy traveler and trying to make the most of the trip in 1 week.

It would help to know where you want to go in Italy. I assume you know how to get to Athens. There are flights from Athens to Venice and to Rome.

There are ferries from Igoumenitsa and Patras to the Adriatic Coast of Italy. The Italian ports are Ancona (where you can visit delightful hill towns in Le Marche, where I live); or Brindisi (near Lecce, Otranto, and other places in the far southern "heel" of Italy). I don't know how easy it is to get to Igoumenitsa or Patras from Skiathos.

If you don't want to rent a car in Italy, it might be best to fly into Rome, where there are lots of transportation choices. I could tell you how to get around by train or bus from Ancona, but I would need to know what you want to do in Italy. Beaches? Medieval towns and castles? Hiking? Great Italian food?

Thank you for your response. As I'm flying to/from Athens from Chicago...then to/from Skiathos from Athens...I'm more interested in transportation that do not involve air. I'd love to take train from Athens to Venice, train to Rome, then south to ports where we could take ferry across then find ground transport. Regarding Italy, yes to food and beautiful countryside but no to beaches or hiking. Did I mention that I'm a senior citizen? If you live in the boot hill area I would love recommendations on accommodations, foodie options or other suggestions.

Natasha, I hope this doesn't come across as rude but you really need to have a clear map in your head for this journey. To travel from Skiathos overland to Venice, then through Italy (and return?) is a very long journey (I've done it both ways but neither recently) and would take a chunk of your one week. And bvlenci lives in Le Marche, not southern Italy. I suggest you start by checking routes using google maps and rome2rio and go from there. Both Italy and Greece are gorgeous countries with an endless amount to enjoy. I suggest that if you only have one week, that you choose somewhere within Greece (or maybe Macedonia or Albania) and make the most of your time that way. Italy will be there another time.

However, if you do decide to do this journey overland, I think going north from Greece overland would be more scenic and interesting (but also long).

Since you have only a week, going by land or sea, to/from Italy, from/to Athens is not going to net much time in Italy for the person who has not been to Italy. They still won’t have been to Italy. You may already be doing some flying, but if they want any time in Italy, it would be best to fly someplace and spend a week in that area. Had you not considered multi-city, into Rome, Venice or Milan and home from Athens?
If you must arrive and depart from Athens, immediately upon arrival in Athens, go straight on to Italy (or Skiathos) and put all time in Athens at the end of the trip.

Do I understand that you need to return to Athens after your time in Italy? If so, and if you don't want to fly, I think you should forget Italy and visit some nice destination in Greece.

Getting from Greece to Venice by ground transportation will take several days. I don't think it can be done by train at all. You would have to pass through Bulgaria, Bosnia, Croatia, and Slovenia; or Macedonia, Kosovo, Serbia, Croatia, and Slovenia.

Here are the suggestions using Google Maps, Rome2Rio, and the German rail website, Deutsche Bahn.

Google: 12 hour bus ride to Sofia (Bulgaria) followed by a 10- hour bus ride the next day from Sofia to Ljubljana (Croatia) followed by an all-night bus ride from Ljubljana to Venice.

Rome2Rio: train (5 hours) from Athens to Skopje (Macedonia) followed by a 16-hour bus ride (Saturdays only) to Venice Mestre.

Deutsche Bahn: train to Patras, changing trains in Kiato, then a 31-hour ferry ride to Venice.

The ferry makes the most sense, but I think I'd prefer to take the ferry to Ancona, which is only a 20-hour trip, and proceed from there by train.

In all cases, this would be an exhausting trip, and by bus it would have been too much for me even when I was young. And passing through the Balkan states by bus might be hair-raising.

I agree with bvlenci that this is a multi-day journey. We've done it several times (all a long time ago when we were young) but only once without stopping (Ioannina to Igoumenitsa to Rome) and we were exhausted at the end of it (we only did it due to a time pressure). When we took the land route through Yugoslavia (as it was then) it was by train but still took two days (and we were heading to Vienna which is easier). That trip was accidental as we had an unexpected change of plans mid trip. I would not even consider this by bus (even if I were 25 again).

If you decide on the ferry, then I would head from Skiathos to Volos to Igoumenitsa to Italy. If overland, check whether the ferry from Skiathos to Thessaloniki is running.

But I re-iterate, you'll have a better time if you stay in Greece and leave Italy for another trip.

You have just 1 week.
If you want to see italy, you must fly.
If you want just enjoy the travel to the Italian border and back without visiting Italy, you may check solutions like:
Skiathos - ferry - Volos - bus - Kalambaka - Ioannina - Igoumenitsa - ferry - Bari or Brindisi - ferry - Patras - bus - Athens