Your first day May 11 is a long travel day so don't expect to see or be awake for much of Venice that day. That leaves you 1.5 days in Venice. I would add a day in Venice.

Forget CT as a day trip from Florence, save that for another trip.

Before you make any purchases at Tamburini, be sure to check what products can actually be imported from Italy to your home country. Just because the items are vacuum-sealed does not meant they will be allowed in. Many people make the mistake of buying vacuum-sealed cured meats at the duty free shops at the airport in Italy, only to have them confiscated when they arrive in the U.S.

Bologna Centrale train station has a left luggage room where you can leave your bags while you visit the city for the day.
http://www.grandistazioni.it/cms/v/index.jsp?vgnextoid=0e08d8a55b4eb110VgnVCM1000003f16f90aRCRD

<but I read about heading to Tamburini in Bologna, where you can get vacuum-packed delicacies to take home with you>

You can get vacuum packed food in any and every supermarket, without heading off to Tamburini. As ellenem says, check what you can and can't take home.

With the time you have I would skip CT - you will be having a great time along the water in the Amalfi coast. And I would add a day to Venice either from Florence or Rome. Another great daytrip option from Florence is Luca. But overall looks like a very good plan! Enjoy!

I think your plan is basically OK because you have a limited number of bases and are planning day trips. I actually think you there's a good possibility you won't end up wanting to take that many day trips - your overall time is not that much. You have one full day in Venice - plus a few hours the evening you get there, and perhaps a few hours in the morning before the train to Florence. But that's enough to get a taste of Venice, especially if you don't feel the need to spend hours on lines to go into things.

Then you have three days in Florence, plus the afternoon/evening of your arrival day. But you mention four places you want to go on day trips. Don't you want to see anything IN Florence? They are all worthwhile daytrips, and easy enough to do from Florence but either some of them or Florence itself is going to get shortchanged. I think Siena is the most worthwhile of the ones you mention. Bus is definitely the way to go (it arrives in the old town, the train arrives on the flats below and you need to get a taxi). If you like long day trips I think it's possible to go by bus from Siena to San Gimi, then back to Florence, but that would be a long day.

Your four nights in Sorrento is a minimum to see the places you list (which are all really wonderful). Perhaps to maximize time you could see Pompeii on the way there or back and not make it a separate day trip. Do a search here, I'm pretty sure people mention a left luggage option, I know lots of people do in en route. We did it as a day trip but we had 8 nights in Sorrento.

With four days (plus an arrive evening) I doubt you'll want to do a day trip from Rome, but if you do Orvieto is a good one.

Just do your research and prioritize what you want to see, and be flexible enough to say 'this place can wait till next time' if you find there is more to see in each stop than you think. But I think your plan looks good because it is open to this flexibility, the people who plan to move hotels every night or two are the ones who risk a trip that's just a blur. Yours is quite reasonable.

Where is the best place to rent a car in Florence for 1 day?

I will be removing 1 day from Rome and adding a day in Florence.

Check out the Mercado Centrale in Florence for wonderful vacuum-packed goodies similar to what you can find at Tamburini, but as commented earlier, don't expect to be able to bring cured meat back to the US, regardless of packaging.

I couldn't agree more with your choice of San Gimignano and Siena to visit. My wife and I LOVED them both. We liked Florence, but the smaller towns have a better feel.

If you're thinking of seeing Greve, Siena and San Gimignano in one day by car, a one-day car rental may not work. It's a minimum of 4 hours of driving, at least another 30 minutes for parking and walking into the towns, time for lunch, and at least 1-2 hours in each town seeing the sights. That adds up to probably 10 hours if you're disciplined with your schedule but likely longer when you see how much there is to see (esp. in Siena).

I know of at least one rental office in Florence (via Borgo Ognissanti) that opens at 8:00 a.m. and closes at 7:00 p.m. (Mon.-Fri. only), but you probably wouldn't/couldn't drive away until 8:30 and might not make it back by 6:45 if you encounter any delays.

You'd be safer renting the car the afternoon before your driving day and setting up the return for the morning after the driving day. You'll lose a little time picking up the car that afternoon and parking it somewhere overnight, but you would be able to hit the road early on your driving day (and avoid the ZTL which starts at 7:30 a.m.). If you get back to the rental office by 6:45, then you'll at least save one night's parking charges and not be encumbered the next day with the need to turn in the car. If you return to Florence after 7:30 p.m., you'd avoid the ZTL again. Sunset will be at about 8:30 p.m. at that time.

It's easiest to avoid the ZTL if you get a car at the airport (shuttle bus from the train station). A one day rental often costs as much as a three day rental.

Where can I park my car if I do rent it the afternoon before in Florence?

Now on to Hotel Info:

I am looking for some recommendations on hotels in Venice, Florence, Sorrento(or Praino), and Rome.

I would like a place that is no more than $175/night in Venice and Sorrento or Praino and no more than $150/night in Florence and Rome. For the Florence hotel, I would probably want parking.

I am looking for hotels where breakfast is included.

In Venice I would like either San Marco or San Palo.

Re: hotels, are you traveling by yourself? If so, are you open to a single room? These are common in Europe and are smaller and cheaper than a double/twin.

In Venice we stay away from Piazza San Marco and the Rialto. Too crowded during the day. We like Dorsoduro, but San Polo is okay.

>>>Where can I park my car if I do rent it the afternoon before in Florence? <<<

You would find a parking garage outside the ZTL, but it will cost 20-40€ per day/night. You will have to figure out which ones aren't in the ZTL.
http://www.firenzeparcheggi.it/index.php?id=2

>>>I am looking for hotels where breakfast is included. <<<

I've rarely encountered a hotel in Italy that didn't provide at least continental breakfast (that is all many provide) even if it means giving you a voucher for the bar/cafe across the street. Breakfast at many places will be very basic - coffee/juice and cornetto.

Use www.venere.com to search for hotels - you can filter by price, location, etc. And start thinking in euros, not dollars. At today's exchange rate, you are looking at a room for $115 in Florence and Rome. That could be tough if you want a view.

If you are going to stay in Praiano (note the spelling) instead of Sorrento, you should see Pompeii on your way to or from the AC. There is left luggage right near the entrance to Pompeii. To get to Capri from Praiano, you will need to take the bus to Positano and then a ferry to Capri.

You have an ambitious adventure...We did the same several years ago..Here is a heads up. Venice is easy to get around. Most buildings (even tucked away down alleys) have directional signs to the Rialto Bridge or to Piazza San Marco. So you can always regain your bearings....However...We found Florence to be very challenging. Street names change every couple of blocks...bring your walking shoes...Keep map in hand...You are going to have a blast. Enjoy!

A hotel with parking in Florence for 110 euros is probably not going to be near the main sights. Do you want to pick the hotel based on parking, location or budget? Even if you find a hotel with parking, it may not be free.

Unless I'm missing some feature of the website, I don't find venere.com very helpful when looking for a hotel with parking. Tripadvisor.com has a search option for parking.

If you're now staying in Florence for 4 nights, you might consider an apartment and may find one with parking.

Can I politely say it doesn't sound like you're doing any research of your own? Could you at least make a short list of hotels in each place that fit your criteria and then ask for comments? We don't know anything about your needs/wants/preferences other than budget (and now, in the case of Florence, parking).