I would recommend taking advantage of the streetcars.
For one, I would definitely suggest taking the St. Charles streetcar Uptown. While you would enjoy a tour of Uptown, just getting on the streetcar and heading up the Avenue is marvelous if you haven’t done it. (As the Doobie Brothers once observed, “just take that streetcar that’s going Uptown.”) On St. Charles you’ll see a parade of different architectural styles, including churches, homes, schools, and other places. The streetcar is public transportation, so you can get on and off as you want, although they aren’t as frequent as they once were. You can get on from Canal Street, just make sure you are getting on the green St. Charles car.
The are also all kinds of cool bars, restaurants, coffee shops, galleries etc. off St. Charles and Carrollton (which the streetcar turns onto at the end of St. Charles, appropriately named the Riverbend,) particularly in the University Section and nearby. Oak, Maple and Freret are all great. Check them out.
Audubon Park is across the street from Loyola and Tulane Universities on St. Charles. It’s a nice park on the far side of which is the Audubon Zoo on Magazine Street extending to the river. Magazine Street itself further back towards downtown has more restaurants and antique shops.
Tipitinas is a great live music venue on the corner of Tchoupitoulas (pronounced CHOP-i-too-las) and Napoleon Avenue. Napoleon intersects St. Charles, and Tchoupitoulas is as far as you can go to the river.
Also, I would suggest heading up Canal away from the river.
You can also take the red streetcar up Canal Street through Mid City. Some cars take a turn onto Carrollton heading toward the New Orleans Museum of Art in City Park. This is a fine museum which hosts both permanent exhibits and traveling exhibitions. It’s on Bayou St. John at the end of the streetcar line. Besides the indoor exhibits, there is also a cool outdoor sculpture garden.
There are interesting casual restaurants (of course) along the trip down this part of Carrollton and at the end of the line here. Bayou St. John is interesting in and of itself, with the possibility of a boat ride and visits to the Deutches Haus and the Eastern Orthodox Cathedral.
Speaking of Deutches Haus, if you are going in October, on the weekends the Haus hosts a fun Oktoberfest. It’s a bit crowded at times and parking is a bear, but I love it. Of course, it’s also not quite what most people think of when they think of New Orleans, but we do festivals very well - and what is Oktoberfest but a festival?
If you ride a car which remains on Canal, you’ll eventually get to “the Cemeteries.” This is a cluster of cemeteries with above ground crypts and monuments that are fascinating in their own right. It might be worth going on a tour rather than by yourself.
There’s more, naturally, but that’s what comes to mind.