The Marigny and Tremé border the French Quarter to the east and north, and are within easy walking distance. The bus and streetcar will also land you in or around these neighborhoods. Biking is a great way to get around the French Quarter and the Marigny.
Bywater is a little farther out, past the Marigny to the east. It makes the most sense to drive or take the bus or a cab. The No. 5 Marigny/Bywater bus runs along the south edge (river side) of the French Quarter, out to the far edge of Bywater. The No. 88 St. Claude/Jackson Barracks bus runs along the north edge (lake side) of the French Quarter all the way into the Lower Ninth Ward. The ride from the French Quarter takes about 15 minutes.