From Bulbapedia, the community-driven Pokémon encyclopedia.
Eggseter (Japanese: ライズタウン Rise Town) is an anime-exclusive town located in Johto. It is located between Ecruteak City and Mahogany Town.
The town is most famous for its Extreme Pokémon Race. Every year, Trainers flock to the town to compete in this famous event. Among the competitors in one year's competition were Ash and Gary. The competition is hosted by Mr. Shellby and his wife. They own a Pokémon Day Care Center where they raise Pokémon Eggs until they hatch, and then take care of the baby Pokémon. Ash won the race and received an Egg, which eventually hatched into a Phanpy.
Its name appears to be a play on Exeter.