The first time you visit this area on your way to Mr. Pokémon's house along Route 30, a Pokémon battle will be blocking the road and you won't be able to get through. The way will be clear after you finish your errand.
Grab more free berries
The guy in the southern house can tell you about Berry trees and the healing properties of Berries. He'll even give you a Berry for the road. Your Pokémon can hold Berries to heal themselves! You can get another Berry from the tree outside, and there's an Antidote just to the north.
Cut through the grass and stay on the right path to get to Mr. Pokémon's house. Before you go in, grab the Psncureberry from the tree to the left of the house. With poisonous Weedle lurking about, you may need it. In Pokémon Gold not has Weedle, but has Spinarak which is the same danger (it only appears at night).
Mr. Pokémon's house
The old man you've been sent to visit has a houseguest: Good ol' Professor Oak! He'll give you a PokéDex, and Mr. Pokémon will give you what Professor Elm sent you for: the Mystery Egg. As soon as you leave, Professor Elm will give you a call on your PokéGear and summon you back to New Bark Town on the double.
When you get the Red Scale at the Lake of Rage, come back to Mr. Pokémon's house to trade it for an EXP Share. This item gives the Pokémon that holds it a share of the EXP earned in each fight, even if it doesn't join in combat!
If you have the Itemfinder at this point, you'd be behooved to use it in front of his house as well.