For a change of pace, you can visit City Park at sundown and take in a free dusk concert on the cool grass.  Weekly, the neighborhood gathers (and turns out quite a crowd!) for quiet classical music concerts by local performers.  A big favorite for families (including the pooch) to unwind from a busy day or an appetizer for a musical night on the town, the concerts are typically about 2 hours beginning around 7 and held during the summer time.

If you have time, be sure to get out of the French Quarter and even the Garden District. here are a few recommended bars that are not downtown, but are local favorites and worth the trip:

Balcony Bar (Magazine St. at Harmony St. uptown, really cheap specials) - also near a bunch of other bars with varying crowds, and a few good restaurants. a fun time. the upstairs is overall better, great view of magazine st, crowd gets collegiate after about 10pm. The chef/kitchen staff and owners recently changed. 
Circle Bar:
on Lee Circle. Small place, packed late. Interesting live music. GREAT bartenders!
- Alternative lifestyle club oriented to open-minded couples and singles who like to mix it up. Great decor with a dance floor and private areas to conect with others or just people watch.  822 Gravier St
Cooter Brown's on Carrollton Ave near the river. Sample a few of the many beers from around the world and enjoy a muffaletta or po' boy while watching your favorite sporting event on one of the many big screen tvs.  The trip to or from the French Quarter on the streetcar which passes Audubon Park and the mansions of St. Charles Avenue is one of  the delights of New Orleans.
F&M patio bar: on Tchoupitoulas uptown. Gets crazy late. mostly College crowd. wild atmosphere.
St. Joe's - (Magazine St. at St. Joseph St. uptown) - cozy, dark, loungey, great back patio, excellent mojitos. pool table too.
Kingpin - Upperline at Prytania uptown. Great neighborhood vibe. elvis decor. dartboard. hope the hipsters haven't found it yet.
The Saint - (Magazine St. at St Mary in the Irish Channel), empty before 11 or 12. Hip Dive atmosphere. great metal jukebox. love the photo booth.
Snake and Jake's - (Oak St. around Cherokee St uptown). LATE night dive in sometimes-sketchy residential neighborhood but worth finding. cheap, dark, weird, dog friendly
Molly's at the Market (Decatur St. a couple blocks off Jackson Square in the French quarter) - mixed local crowd, great bartenders, slightly off the tourist path. they pour a mean guinness. 
The Whirling Dervish (goth/alterntaive friendly club a few blocks farther down Decatur from Molly's),  usually industrial music. doesn't get going til late (1am)
Pirate's alley Cafe (Pirate's alley off Jackson square in the French quarter hole in the wall, cheap, no tourists!)
One Eyed Jacks' - on Toulouse St in the French Quarter. Has leighties nights on Thurs.  hip front room, music in the back. often has good live music and burlesque.
Tipitina's (Napoleon & Tchoupitoulas St) -this is pretty much THE place to go to see live music. Take a cab, crime has gotten worse since Katrina here.
Deutsches Haus - If you're here at the right time of year, they have beer festivals. It's a tradtional beer garden. Around Canal and Galvez in mid-city.  It  has re-opened since Katrina, but it may soon be demolished to make way for a new hospital project - stay tuned.
R Bar - On Royal St. off Esplanade in the Marigny. Neighborhood bar, great decor and tv's. has attached hotel.
Port of Call - Esplanade Av at edge of French Quarter/Marigny - has strong drink called a monsoon. a good starting point if you're around Frenchmen St. Also has huge burgers and baked potatoes.
Rock n Bowl - On Carrolton just past the Interstate 10, in mid city. It is a bowling alley with a bar and live music. sometimes has zydeco and rockabilly.  The music is fabulous.  Swing night is Wednesdays, Zydeco on Thursdays and Friday and Saturday more live music.  This is a good place to go dancing swing or zydeco on the abovementioned nights.  And, because of their restaurant license, the place is nonsmoking.  This place also has a parking lot or they will happily call a cab for you.  Cover is often $5-$10 for live music and you do not have to bowl to enjoy the music.  Tables and chairs are available for seating as well.
The Columns - St Charles Ave at General Taylor uptown. Good for happy hour or watching parades. $2 champagne on Friday until 7pm. awesome atmosphere. look for the garden around the side.  beautiful old hotel, very New Orleans!  They often have live music on Thursday, Friday and Saturday nights from 8-11pm
pal's - st philip at rendon (off jeff Davis in mid city) - great dive in mid city. has air hockey. and an awesome picture in the ladies room (its a surprise.) gay-friendly. great prices.
McNulty's/The Bulldog - 2 bars next door to each orher, in mid city by the cemetary, city park ave at canal st... bulldog has outdoor seating and a very good beer selection and free nola themed pint glasses with beer purchase on wednesday night.
Saturn Bar- St Claude av not too far out of the French Quarter, in the Bywater. Take a cab and be careful as this is not the best neighborhood, if you get lost on the wrong side at night.

Frenchmen St: Maison, The Spotted Cat, d.b.a., Snug Harbor, The Blue Nile and many other new clubs.....all are fabulous music venues on the 2 blocks of this street.  Friday is a happening scene there, especially since Katrina!  It's where the locals go; cabs are easy to get there or if you are in the French Quarter, you can walk there.

Please keep in mind that since Katrina many things have changed!