We stayed at the Drury in April. Great hotel, and reasonably convenient location. Perks of staying at Drury can't be beat. We took a taxi from the airport. The Drury is close enough to the French Quarter that it is included in the flat rate for taxis between the airport and the French Quarter. I don't remember the price, but you can easily find it by googling. Many of the taxis were mini vans, so that would cover the 5 people. There's a taxi stand right outside baggage claim, and the line moves quickly. Buy a Jazzy Pass once you're in New Orleans for the length of time you will be using the transportation; it'll cover bus and street car. There's a list on the website for Jazzy Pass of where you can buy them. I bought ours at a pharmacy. Don't remember if it was Walgreens or CVS, right in the French Quarter.
Is it the Jazz and Heritage Festival that you're going to? We went to that one and it was AMAZING.
We loved the food at Gumbo Shop. Pat O'Brians is also a lot of fun. The jazz brunch at Court of Two Sisters was excellent. The fried chicken at Brothers really is the best there is (and it's conveniently located on the walk back to the Drury...cheap too). The WWII museum is incredible, and the museums in Jackson Square (Presbytere and Cabildo) are both very well done. Jackson Square is neat to walk around. If you like jazz music you MUST see a show at Preservation Hall. Such a cool experience. Pay the extra for the Bigshot Tickets. It's completely worth it to not have to wait forever in line in whatever crazy weather may pop up. You can also bring drinks in, so don't hesitate to stop by the courtyard bar at Pat O'Brians and get a hurricane. They serve them there in a to-go cup so you can walk anywhere with it. No open container law, at least in that part of the city.
Weather in New Orleans in April can be crazy. We saw 90* and sun. We saw 70s and (normal) rain. We saw torrential downpours that were part of storms that spawned a tornado in another part of the city. Be prepared for EVERY kind of weather. Program the number for a cab company into your cell phone (TA recommended United Cab New Orleans if I'm remembering correctly).
Also, total luck of the draw, we were there during Navy week when several military ships from the US and other countries were in port and open for (free) public tours. We stumbled upon this. Since it was also April, might be worth googling to see if it'll happen while you're there. VERY cool to see and the active duty folks were SO excited to show off their ships.