Where do Pokemon go?

To the PC in a Pokemon Center.
Pokemon can go to many places within the 'Pokemon universe'. Primarily, Pokemon are wild animals which live in the natural environment. The type and abilities of Pokemon influence what sort of places each Pokemon prefers and as many Pokemon can be found in the forest as others in the sea or the city.
Pokemon who are captured by trainers either accompany the human on its travels or are sent to a Pokemon storage system available through a Pokemon Centre PC. Pokemon who travel will most likely go to major cities which contain Pokemon Gyms. Pokemon who are stored are likely to end up in a sort of ranch or preserve as seen in the Pokemon anime, where Ash Ketchum's Pokemon are sent to live with Profesor Oak.
Legendary Pokemon have greater abiities than normal Pokemon and are thus able to travel on a wider terrain. Particular Pokemon can roam the skies or even outer space while others reside deep underground. Of course, there are other Pokemon who can live in cyberspace or undiscovered dimensions.
However, considering that Pokemon are a fictional creation, it is fair to say that they may 'go' anywhere the imagination may take them.