Canal Street Ferry: Free for pedestrians; runs across the Mighty Miss to Algiers Point and back; takes about 30 minutes round trip and offers great views of downtown and the Quarter; runs until midnight.
St. Charles Avenue Streetcar: $1, correct change required. Runs from downtown through the Garden District, past Audubon Park and Tulane University. Desire, as in "a streetcar named..." was part of this system. "Stella! Stella!" Sorry, I digress.
Audubon Park: A huge park; great place for kids to blow off steam with playground equipment and lots of open space; bring a football and have a picnic. Very limited parking on the street so this is best combined with the streetcar. Note: DO NOT go in any parks in the Big Easy at night!
Audubon Zoo: $10 adults, $5 kids (12 and under). Off Magazine St. between Audubon Park and the Mighty Miss. Not exactly a cheap recommendation, but an old, well-maintained zoo the kids will love. It has an extensive area on animals of the bayou.
Confederate Memorial Hall: $5. 929 Camp Street. Old museum with lots of uniforms, weapons, photos and documents; a must for anyone interested in The War Between the States. Hop off the streetcar at Lee Circle. Other museums in the area include Ogden Museum of Southern Art, the National D-Day Museum and N.O. Contemporary Art Center, but I haven't explored any of these (yet).
Central Grocery: 923 Decatur Street, near the French Market. N.O.'s best muffuletta. This is delicious N.O. fare without the Commander's Palace price. Unless you're starving a half-one will probably satisfy you.
French Market: This is a real working market, not just a tourist trap. Trade has been going on here since the 1700's. Stroll through stalls of just about everything for sale including food, jewelry, and even Sugar Bowl souvenirs. Also the very rare and much sought after public restrooms are located at the market. My wife will use this one, so they must be fairly clean, especially by Big Easy standards.
Café du Monde: I know, I know everybody knows about it, but I had to mention it. Load up on beignets and feel your arteries harden. Also if the coffee with chicory isn't your deal, they have ice cold milk. Excuse me, I'd better go take another blood pressure pill.
Hilton New Orleans Riverside: On game day go sit in the lobby (wearing garnet darn it), order a beverage and soak up all the dirty looks. This is traditionally home to a vast number of the SEC teams' fans.
I hope I have made some decent suggestions that will help ease your wallet. You really can have a great time in the Big Easy on a budget. I am old so I'll let more knowledgeable Noles give advice on Hand Grenades, Hurricanes and warm beer in plastic cups.
Steve Pigott (aka 90Nole, formerly 89Nole)