For reasons of safety and speed if you are coming in late at night, I would take a Lyft or Uber (should be about $30-35 from MSY to central NO). The New Orleans public transit system is, to put it mildly, a travesty. Fares are cheap, and you get just what you pay for: infrequent and often unreliable bus service with a route network that is very deficient, or more frequent but very slow streetcar service with a route network that is geared toward tourist-frequented areas. If you’re staying in the center of town, walking during the day and taking Lyft/Uber at night is likely to be your best option.

For $100 or less you are looking at a private room in an Airbnb, most likely. This can be a very nice way to stay in a good neighborhood and take advantage of the host’s knowledge of the city. Airbnb gets a lot of grief from New Orleans residents due to short-term rentals taking residential rental properties off the market and driving up pricing, but if you are in a private room (vs. a complete unit) you are not contributing to that problem.