If you only have two days, then the French Quarter is definitely the place to stay. It is way more than "bars and drinking". We don't drink either, bit we would not stay anywhere else. May I suggest the Hotel St Marie as a nice place to stay. Meanwhile, Herre are SOME of the "must dos" in the French Quarter alone:
-Visit Jackson Square and peruse the offerings of the artists and craftsmen there.
-Stop often and listen to the street musicians and observe the street performers. BE SURE TO TIP THEM IF YOU LIKE THEIR PERFORMANCE. ( For that reason, be sure to bring a bunch of dollar bills, and fives too.)
-Go into the beautiful old St Louis Cathedral at Jackson Square. Again, BE SURE TO LEAVE AN OFFERING to show your appreciation.
-Visit the French Market to peruse the Flea Market and the Farmer's Market and the associated restaurants and shops.
-Take a buggy ride from Jackson Square around the Quarter to get narrated history lesson.
-Eat a beignet at Cafe Du Monde.
-Eat a po'boy sandwich or some crawfish or alligator on a stick.
-Take a walk along the Mississippi River levee.
- Take a cruise down the river on the Riverboat Natchez.
-Take a FREE ride on the Algiers Ferry to get a great view of the Quarter from the river.
-Peruse the art galleries on Royal Street.
-As an alternative at nite, walk over to Frenchman Street to the jazz clubs.
-EAT, EAT, EAT, EAT, EAT, EAT at many of the dozens of superb dining establishments in the Quarter.
-SHOP, SHOP, SHOP, SHOP, SHOP, SHOP in everything from "touristy" shops to high-end places.
-Take a ride on fhe streetcars, which opens up an entire new set of activities OUTSIDE of the FQ!
-Take a tour to visit local plantations or swamps or a "Katrina tour" to understand the devastation and recovery from that terrible event.
And this list has only touched on SOME of the highlights. Others will, I'm sure, add to this list.