Burbank is the closest airport to the wedding reception, but LAX is a much bigger airport and may have more flight availability.
If you fly, you likely will not need to rent a car. Most people visiting LA choose to Uber or Lyft around the city. You may want a car, however, if you plan to explore after the wedding or go up the coast.
If you drive, remember that parking may be limited. The restaurant does offer valet parking, which is $30 for the night. There is also street parking around the hotel.
If you already live in LA or are staying further away, the hotel is a 5 minute walk from the Hollywood and Vine Station on the Metro Redline. Just remember that the metro is not always safe after dark in LA.