We have fourteen days in Italy. Our itinerary so far is three nights in Rome, and then two days to fill before booking in for seven nights in Minori on the Amalfi coast with two other grilfriends. We will then stay one last night in Rome before flying home to Australia.
I will be travelling with a friend, we are late 30's, and not really into war memorials. We would like to squeeze in as much as we can in those two days, either by car or fast train between destinations. We love markets, shopping and seeing character filled streets and towns.
Wondering whether it would be too much to travel from Rome to Florence by train, and then take fast train down to Naples (apparently takes about 5 1/2 hours).. May be a bit too long when we only have two days?
Does anyone have any suggestions for an itinerary?

If you don't mind the mobs of tourists the cram into Florence most of the year, it sounds like Florence fits your interests.

The fast train takes less than 3 hours from Firenze to Napoli, although if you are going to Minori, you might want to take the train to Salerno and proceed from there.

But you might also consider extending your time in Rome if you are arriving from Australia jet lagged. You will barely have time to see the town in what will effectively be 2 days once you get some rest, and if you would like to shop, go to markets and explore some character filled streets, Rome is the more outstanding place to do that.

If you would really like to see Florence but to avoid a hotel switch, you could stay in Rome the whole time and take a day trip to Florence. Booking an apartment in Rome would probably save you some money and get you more elbow room, perhaps even a terrace or a second bathroom.

You could also consider a visit to Naples for two days. The fast train from Rome is only 90 minutes. If you want "markets, shopping, and character-filled streets," look no further!

Naples would be a good option. I just came back from a France and Italy trip last week. Spent five days based in Naples--it is a very vibrant city. You might also consider Capri. It's less than an hour by hydrofoil and is just gorgeous. I can't wait to go back!

Add the 2 days to your Rome stay.
You could do a day trip to Orvieto, Ostia Antica, or Pompeii...or just spend more time in a city with thousands of years of history, architecture and amazing food!

This one is easy - extend your time in Rome!!

I originally thought that extending Rome was the best choice, but really, I think of Florence as the quintessential markets and shopping destination.

Unlike most people here, I pretty much hated shopping in Naples (endless underwear stores) and thought the markets were a bit grungy. The market street where nativity figures were sold had several shops/stalls selling exactly the same foreign made figurines.

I don't quite understand the war memorials comment. Can you explain further?

With only 2 days I would stay in Rome. You could use one of those days to take a day trip to Orvieto, not far and really charming. Or you could also take a longer day trip to Florence, saves the packing and moving aspect for a short stay. I would just not want to train north for two nights, to add more travel time getting to the Amalfi Coast.

I agree -- extend your stay in Roma. OH the shopping! But a day trip to Orvieto would fit your craving to see a beautiful and interesting small town. OR spend the night in the beautiful old centro and travel from there to the AC. I think Naples, while it would be a great city to visit...is still a city. Orvieto is very different from where you are staying on the Amalfi Coast.

Are you planning to visit Pompeii while on the Amalfi Coast? If so, you might spend one of the two days in Rome and the other near Pompeii (Sorrento?) on your way to Minori.

Thank you to everyone who has replied and added a post. I can not thank you all enough.

Why not just spend the two days in Naples? You could see Pompeii from there and not take a day away from your Amalfi Coast visit...

And from Naples, you could also visit Mt. Vesuvius, day trip to Capri or Ischia, day trip to Pompeii...

Is there any way to put all your Rome stay at the end together?

You could go somewhere like Orvieto or just add the nights to Rome and do some day trips (Orvieto? Tivoli?).