PokéCenters
From Dexnet
Pokémon Centers, usually shortened to just PokéCenters, are a chain of facilities throughout the world, owned by the widely known and renowned Joy family. Along with establishing and owning the PokéCenters, the Joy family is mostly famous for being full of redheaded women who look eerily alike (some even speculate that it's really just a family of clones). Every Center is overseen by at least one Nurse Joy as a head nurse, though other nurses outside of the family may be present.
PokéCenters provide many essential services to Pokémon trainers. The most obvious and basic is their role as a Pokémon hopsital. Every PokéCenter has state of the art facilities for the care and treatment of injured Pokémon. This service, like all PokéCenter services, is provided to trainers free of charge.
PokéCenters are also vital facilities for the trainers themselves. A valid Pokémon License can get you a bed for the night in the hostel and a meal at the cafeteria. There's also a lobby in which trainers can congregate, video phones for the public use, and a PC with access to the Pokémon storage system. Some Centers may even include theatres, cafes, or other open spaces where traveling entertainers and the like can perform for trainers - a chance to relax and take a break once in a while from their heavy schedules.
Smaller towns obviously have smaller Centers. Celadon City's PokéCenter may have ten PCs for trainers to access and a lobby full of vending machines as well as separate waiting and emergency rooms, with dozens of nurse staff on call, while Pallet Town's PokéCenter has just one Nurse Joy at the front desk, and only one PC in the lobby which doubles as the waiting room. No matter the size, all PokéCenters can be easily recognized from the outside by the giant P on the building.
In addition to these services, PokéCenters are also responsible for issuing and renewing Pokémon Licenses, as well as giving out starter Pokémon to new trainers. License classes will vary in frequency depending on the needs of the center. Small towns may only have a license class once a week, while larger cities may have them daily, twice a day.
Starter Pokémon are given only to newly licensed trainers and are given free of charge. The starter Pokémon available varies from region to region. It's also based on a first come first served basis, so if a trainer has the misfortune of being the last in line, they may not be able to choose, and in smaller cities they may not even get a starter at all.
The most important thing about Pokémon Centers is that they cannot refuse service to any Pokémon or legally licensed trainer. If an unlicensed person brings in an injured Pokémon, the Center is required to heal that Pokémon, though they are not permitted to turn it back over to the person who brought it in if that person does not have a valid Pokémon License. They cannot refuse any services to a trainer with a valid license, which means that even Team Rocket members who come in uniform will be provided services like any other trainer who comes in, though they may be treated with personal disrespect depending on the person dealing with them.
PokéCenters also handle license renewals in addition to initial license issue, and (as long as there's no official record of the license being revoked) they cannot refuse this service either, no matter the nurse's personal opinion of the trainer. This means that, yes, Team Rocket members could walk into a PokéCenter and have their license renewed, though they may suffer some hassle for it with the staff.
PokéCenters also issue PokéDexes, and provide PokéDex information upgrades through the PC system. A lost PokéDex can be replaced for a fee (the lost one has services cancelled, much like a stolen credit card), but a replaced PokéDex will not contain any of the information stored in the lost one.