Instead of relying on a particular Pokémon to take you around from city to city, there is a useful service in Pokémon Sword and Shield called the Flying Taxi. You will get it quite early in the game and it will make traveling between cities a lot easier.
You will receive the skill shortly after making your appearance in the opening ceremony as the Gym Challenger in Motostroke. After finishing the celebration and making your way out to walk through Route 3 to tackle your first gym, you gain the skill. You have received unlimited access to the Flying Taxi service, which will involve a Corviknight spinning you around.
To use it, all you need to do is open your map in your inventory by pressing the "X" button on your Nintendo Switch and going to the City Map option. You can fly to any location on the map with a small wing symbol next to it.
However, you can only do this for the cities you have visited. If you haven't visited one, you must first walk to it the old way before adding it to your taxi service.