Downtown Disney is mostly stores and restaurants, so you can window shop and eat. Sometimes they have live music but I'm not sure what time that happens. Goofy's is a great idea, and since you're already going to be at DLH you could get Dole Whips at Tangaroa Terrace.
At the end of March the egg hunt will still be going on in DTD:
A Hippity, Hoppity Good Time
Celebrate spring with the return of Eggstravaganza—a special “egg” search taking place throughout the
Disneyland Resort from March 11 to April 9.
At this fan-favorite event, Guests search high and low for characters painted on eggs. A Donald Duck egg could be placed on a window ledge or in the nook of a doorway, while a Goofy egg may be spotted next door. Can you find them all?
How to Join In the Fun
1. Pick up your map and stickers for $9.99 plus tax at select merchandise locations.
2. Have fun searching for hidden “eggs” themed to Disney characters and placing the corresponding stickers on your map.
3. When you’re done, return your map to a redemption location and receive an eggs-citing keepsake: one of 6 collectible themed keepsakes—which you’ll receive even if you don’t complete the entire quest.
Pick up your map at a sales location. Then let the search begin! After “egg” searching, return your map for a keepsake at a redemption location.
Maps differ between Disneyland Park, Disney California Adventure Park and the Downtown Disney District. Make sure to search in your map's designated location.
Downtown Disney District
Sales Locations:
Redemption Locations: