June 24-July 5th first time in Italy, PLEASE help

There are more than museums to see in Florence!! So much more! Florence is small but with something to look- at, at every street's corner and vert walkable. Rome is big.
Your Holiday is not long. I think that for
- Venice: you would need 3 nights at the very least (2 full days).
- Rome : 5 nights (4 full days)
- Florence: 3 nights (2 full days: if you are not a museum goer).
- Amalfi coast (if you really want to rest and do the most of it, visit Capri and Ischia, Sorento). If in the area, visit Naples, such a beautiful city although hectic! would choose Ischia as a base in this area but maybe you will not like an island because you will always need the boat to get out. I love Ischia and its musical festival in the summer. I think it is nice to take a place where you can take a Traghetto.

In fact, with such a short time, I would do

Rome (4 full days)
Naples ( 1 full day) : take the open deck bus to get a good feel of the city.
Do eat a pizza! Try one with fresh tuna fish or spada)
Positano, Salerno, Sorento, Amalfi, Ischia, Capri

You could do Venice and Tuscany another time.

I would suggest writing down each city you want to visit and the hours by train to reach them. Also, include time to reach the airport after you're at the Amalfi Coast. Then decide how much time you're willing to spend on trains vs. out exploring cities & countryside. If you're happy with your decision, it's your vacation and enjoy it! : )

Personally, we're not big fans of Florence other than the fantastic museums (we've been there twice) compared to so many other locations in Italy.

It is not a sacrilege to skip Florence! I do think Venice at two nights and Rome at 3 are a bit light, but if all you have is 9 nights on-the-ground, so be it is you really want to see the Amalfi Coast.

Train is perfect. Only 3 1/2 hours Venice to Rome. Go online at Captain Train and buy tickets as soon as your plans are firm and you can save some money with advance purchase discounts.

Rome to Naples is a bit over an hour on the train (same suggestion on advance reservations) but it takes additional time to reach the A.C. It's about 75 minutes to Sorrento by the Circumvesuviana train. To get to Positano, you then need to change to a bus. A suggestion, though we've not done it, is to look into a private transfer from Naples to Positano if you decide to stay there. Rick Steves' book should have info on that. Time and hassle saving. Or stay in Sorrento. It is lovely and a good base for Capri and Pompeii.

I agree with Laurel. You can save some hassle with a private transfer from Napoli to the Amalfi Coast. Note that Sorrento is not part of the Amalfi Coast.

June 24 to July 5 is 11 nights all up. Does this include travel?
I am thinking you lose one night to travel.

With ten nights ...
Venice (3 nights)
Rome (3 nights)
Sorrento (4 nights) - with excursions to Capri, Positano, Pompeii, Naples

Thank you everyone, I'm going to speak to my travel agent and will keep all your reccomendations in mind
Any specific hotel suggestions ?
I'm looking at hotel Monaco and grand canal in Venice
Hotel delle Nazioni in Rome
And thinking between hotel pasitea or hotel Poseidon in Positano

Do you think we are staying in the good locations ?

Assuming you want to visit the cities you mentioned (Venice, Rome, Sorrento), consider that the last night must be spent in the city you are departing from and that city is likely Rome (Airport code: FCO).
You should consider this sequence:
Arrive VCE
Visit Venice 3 nights
Train all the way to Naples, then commuter to Sorrento (plan 7 hours en route)
Visit Sorrento Peninsula (incl. Amalfi Coast, Pompei, Capri, etc) for 4 nights
Train back north to Rome
Visit Rome for the last 3 nights
Depart from FCO

We are flying in from New York to Venice and flying out of Naples

A few thoughts to add to the others......

The three places you mentioned are a good introduction to Italy, but I'd highly recommend using Sorrento has a home base to visit the Amalfi Coast. Positano has no rail connections and if you're planning to do a lot of touring, Sorrento is a better choice. It will also be much easier transport from there to Naples airport when you depart (use the Curreri Viaggi Bus). Staying in Sorrento fits your criteria of not "wasting a lot of our time travelling from one city to the next." If you stay in Positano, you will be spending more time travelling from one location to the next.

I tend to agree with the Itinerary that David posted. Spending three nights in Venice is good, as you may need a day to recover from jet lag and that will also provide an opportunity to "acclimatize" to Italy since it's your first visit. Three days for Rome is "light" but if you plan your touring carefully, you should be able to see the main sights. Keep in mind that you'll only have about 2.5 days, since the trip from Venice will require about half a day. Four days in Sorrento will allow you to take a few day trips to Capri, Pompeii, Herculaneum and Positano (which you'll have to access by Bus, Taxi or private transfer). As with Rome, you'll only have about 3.5 days for actual touring.

For the trip from Rome to Sorrento, you have a couple of choices. The first part of the trip from Roma Termini to Napoli Centrale will be via Freccia high speed train. That part is very easy. However, for the trip from Naples to Sorrento, you'll have to go downstairs to the Napoli Garibaldi station and transfer to the Circumvesuviana train, which has a bit of a "colourful" reputation as a haven for pickpockets and scammers. If you're cautious and wearing Money Belts, you should be fine. Note that the Circuvesuviana has several routes so be sure to board the correct train for Sorrento (it also goes by Pompeii). If you'd prefer a more comfortable trip for that segment and your budget will allow, you could arrange a private transfer from Naples to Sorrento using the Monetti Taxi or others (I believe there are other suggestions in the guidebook).

If you want to "make the best out of this trip", I would highly recommend packing along a copy of the RS Italy 2016 guidebook, as that has an enormous amount of information on sightseeing, hotels, restaurants, transportation, etc. I'd suggest using the hotels listed in the guidebook, as they are all reliable and re-checked every year.

As this is your first trip to Italy, you'll need to be aware of the potentially expensive "caveats" when using public transit. If you need further information, post another note and I'll send my usual "boilerplate" on the subject.

Well I definitely know there is no other city like Venice. If you want to splurge on an extra day at some particular destination then let it be Venice. You'll never regret having an extra day there.

To give you a little 'extra' time in Rome, you might like to take a morning train from Venice to Rome, and an afternoon transfer from Rome to Sorrento.