Italy in May 2020

Here is a guideline where to stay in Amalfi Coast:

Where to stay in Amalfi Coast first time – Sorrento

Where to stay in Amalfi Coast on a budget – Salerno

Best area to stay in Amalfi Coast for nightlife – Positano

Coolest place to stay in Amalfi Coast – Praiano

Best neighbourhood in Amalfi Coast for families – Maiori

To arrange Itinerary in order:

Fly into Naples, from there you can easily reach Amalfi Coast as your first stop on your tour.

Then after Amalfi Coast head to Rome.

Continue from Rome to Florence / Tuscany

Do Florence to Bologna

Bologna to Milan

Fly out of Milan to go home

You might also do it in this order:

Fly into Milan: train to Bologna,
Florence/Tuscany
Sorrento/Amalfi Coast
Rome - fly out of Rome.

Do your 15 days include both the day of your flight to Italy and the day of your flight home? It's more accurate to count the number of nights on the ground you'll have in the country. If you're including your travel days, you don't have as much time as you might think you do.

For a first-timer with 5 nights/4 days to spend in the AC/Sorrentine region. I'd choose Sorrento. It sort of depends on what you want to do when you get there but it has the most transport options (although Salerno has train service too; Positano does not), is a cheap and easy hop to Pompeii, has good ferry service, etc. It's one of those personal preference things but we would have been bored in Positano for very long; not much to do and felt too upscale-resort-like to us. Pompei (if that's on your list) is also more time-consuming to get to from there.

You might also want to stay in Amalfi. Less touristy, centrally located, transportation hub for buses and ferries. Easy to visit Positano, Ravello, Praiano, etc. I stayed in the Villa Annalara, only 6 good sized rooms with a terrace overlooking the town and the sea.

We will be in Italy for 15 nights.
Thank you