I really prefer the explore feature currently only available while events are up, ie: Halloween ebilia egg hunt.
This is more interesting than simply refreshing and would love to see it as an everyday option for non-seasonal eggs. the ability to find small bags of tu instead of just a random event could also be implicated, or squishies, etc.
A new thought may be the ability to find multiple eggs or have creatu sightings, not the ability to collect (though that would be nice while exploring the forest) but maybe a glimpse and an avatar to go a long or some clothing item. Just a thought.