It depends on where you're going. New Orleans is a very walkable city, and ridesharing is a good option as well. When you're coming in from the airport, a typical cab may be more cost-effective than rideshare. The streetcar is awesome, but it is slow and doesn't operate on the most regular of schedules. Download the Le Pass app to buy virtual streetcar tickets or make sure you have exact change.
Your guess is as good as ours! Typically, the weather in December is mild and can range from mid-40s to mid-60s. Plan to bring layers as it can be chilly at night but warm during the day. Keep an eye on your favorite weather apps while packing your bags.