The best way to get from Disney's Art of Animation Resort to Disney's Boardwalk is to take the bus to Disney's Hollywood Studios. Once you arrive at the theme park, locate the Friendship ferry boat launch, which is not far from the entrance of the theme park. From here you will sail to Disney's Boardwalk after two stops at the Swan and Dolphin hotels and Disney's Yacht and Beach Club Resorts. The boat ride takes about 20 minutes once you've boarded the boat. You can also walk from Disney's Hollywood Studios to Disney's Boardwalk. Once you make to the entrance of the park, look for the walking path along Crescent Lake. This walk is about 20 minutes.
If you find that you are running behind a bit, you can always use Uber or Lyft directly from Disney's Art of Animation Resort to Disney's Boardwalk Inn. Once you arrive at this resort, walk down the steps, and you'll be on the Boardwalk! There is an extra fee for this service for it fairly minimal.
Enjoy your time and dinner at Walt Disney World! If you more questions, stop by and visit with us again!