I'll be staying in a little boutique hotel in what looks like will be right on the edge of French Quarter. How's parking there and around the rest of New Orleans? I'd like to be able to visit Magazine Street, Frenchmen Street, the City Park area, etc, and was wondering if it would be wise to rent a car, use public transportation and/or cabs.
Unless you don't mind paying for parking all the time, I wouldn't suggest renting a car. In and around The French Quarter is near impossible to find parking in, and at times, impossible to even drive through, and when there is parking around the edge of the French Quarter, it's still metered.
New Orleans is actually a very walk- and public transportation-friendly city. There are buses and trolleys to take. I just used the public transportation option on the Google Maps app on my iPhone to find the stops, route and the time.
The places that you listed -- Magazine Street, Frenchmen Street and City Park are all accessible by those means of transportation. You can walk or bus to Magazine Street, walk or catch a bike carriage ride to Frenchmen Quarter, and bus or trolley to City Park.
Plus, it's way more fun to walk and explore, and you see so much more when you're not driving :)
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The cheapest way is to use public transportation. Cabs and rental cars would be more expensive, but more convenient. The cheapest car at Rental24H is from Alamo, its price is $68 per day. And, don't forget about the parking charges. If it's not expensive for you, it will make your trip less stressful.
You can rely on the taxi service. You will not have a problem finding a taxi from the French Quarter. Parking is pretty bad. You can park your car on the street, but I wouldn't recommend it. There are several parking garages where you can park for days for $20 or so a day.