OP, the photos you posted look more like some of the more historic small river towns, such as St Francisville or Franklin; New Orleans' density doesn't quite shake out that way. (Though actually you might find something close to that look in the older part of Hammond near the university. Hammond is a small city on the north side of the lake, halfway between Covington and Baton Rouge.) The front-picket fence look dripping with plantings is something you do find Uptown and in the Garden District at times, but there, your house is going to be built much closer to the lot lines, so there won't be a large garden, and also probably not a garage for your vehicles unless it opens off an alley behind the house. Also, these days, a lot of people have cut back landscaping near the street, both for parking and for crime prevention reasons. (There is never enough parking in most of New Orleans, so you will almost always see cars parked on residential streets.)
Apologies for the large photos, but I want to illustrate density.
I used to live on this street, which is uptown near Tulane. First the street view, and then overhead so you can see the density.
This is Mid-City; Banks Street, which IMO is one of the nicer streets in the area (most of them other than the main arterial streets are not this leafy and don't have that useful neutral ground in the center. (New Orleanians park their cars on those strips when it storms, which helps get the cars above normal flood level.) Note the long, skinny "Shotgun" homes visible in the aerial shot.
This set is from Lakeview (the large building at top left in the aerial is Mt. Carmel HS). Note that many of these homes are new since Katrina, which accounts for the dearth of mature trees in spots:
And this set is Metairie very near the Causeway:
Also, just to help our understanding of what you mean by a large house, how large are you envisioning? As in sq.foot/sq.metres? What an American typically defines as large might not be what you define that way. You said you want at least 4 bdrms, but that could be anything from a shotgun house with a converted attic, to a mansion. ((BTW, 2 old styles of house unique to New Orleans are the Shotgun, a narrow house so called because you could fire a gun from the front door to the back door and not hit anything in between, as the doors of all the rooms are in a straight line, or the camelback, which is a house that resembles a shotgun from the front, but has a second story only on the back half. Both of these styles tend to be small homes, but I've been in some 4 bdrm versions of both. Homes in New Orleans (most of Louisiana, really) do not have basements; the water table is too high.))
PS: FWIW, New Orleans has a large Italian-American community; they were the largest family immigrant population to come during the 19thC; (but almost all of them were from Palermo; they are still pretty Sicilian in their tastes. New Orleans has some of the most wonderful hybrid Creole-Italian dishes you could imagine.) Originally most of them lived in the Lower Quarter, and then many moved to the 9th Ward, but by the latter half of the 20th century they left there and began scattering widely among the suburbs. There are several St. Joseph's Day celebrations in the area. (Once upon a time there was a nasty feud going between the Italians and Irish in New Orleans, back when the Italians controlled the longshoreman's union and the Irish controlled the police dept., but it was settled long ago, and now there are actually a lot of Irish-Italian joint civic groups.)
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