Savannah -- I assume you want to spend time in the historic district. You really need to stay IN the historic district, though that's a fairly expensive choice. Yes, you can find loads of less expensive hotels outside the area, but PARKING isn't just expensive and difficult, it's non-existant. You could easily drive around for an hour or more and literally find NO parking, especially during spring break. Budget and Savannah don't go together -- the answer here is to bite the bullet and pay for a hotel that'll provide parking in the area you're going to want to visit. You will probably pay a parking fee in addition to the hotel fee. Although I usually love Priceline, Savannah isn't the city in which you should roll the dice. Parking aside, Savannah is a lot of fun, and you'll find plenty of things to do. Once you're parked, you won't need your car.
New Orleans -- This IS the place to use Priceline. With several big hotels just outside the French Quarter, you're likely to win either the Marriot or the JW Marriot (odd that those are within a block of one another) or one of the other hotels near the casino. This is a good area to make a homebase because it's away from the noise and filth of the French Quarter, yet it's within walking distance of everything. I know we paid something like $60/night and were very satisfied with our Priceline hotel; this is the place to make up for the high price you'll pay in Savannah. Parking is also a problem here, so expect to pay a parking fee to the hotel as well.. Again, like Savannah, once you're parked, you're not going to need your car. We personally dislike New Orleans and will not return, but people on this board tend to defend it vehemently and cannot fathom any negative opinion on it.
I can't provide any help with Memphis.
These three cities aren't exactly close to one another. Are you planning to drive this in a single week? According to Google maps:
Savannah to Memphis is 631 miles / 9 hous 26 minutes
Memphis to New Orleans is 395 / 5 hours 49 minutes
New Orleans to Savannah is 683 miles / 9 hours 41 minutes
If we're talking about a single week, I'd say you could do one of these cities thoroughly, or you could do a quick trip through two of them. We're a family that doesn't mind long drives, but this looks un-doable.
Although I see the appeal in doing these three cities, you might be more realistic to pick a couple places closer together. For example, you could do Savannah and Charleston in one week easily. Or you could do Memphis and Nashville. You could do the others during future vacations.
Let me know if you need restaurant suggestions.
