We'd recommend staying at an Airbnb in the area. There are also several boutique hotels in the neighborhood (wythe, william vale, hoxton, franklin guest house) but they are a bit on the pricier side.
Any and Everywhere you can! The food in this neighborhood is amazing. If you're looking for specific recommendations just let us know!
Do Not rent a car. We recommend using Uber or Lyft to get places. Brooklyn also has a ton of public transport options and if you're really feeling the itch to drive in the thunder dome you can get a rental or a zip car easily.