That's up to you, really. I saw you have a ponyta there, one of the many kinds of pokemon that inhabit this world. Typically, most people called "trainers" will travel with their pokemon companions, challenging other trainers and wild pokemon to friendly matches to test and increase their strength.

Other people prefer to stay in one place, picking a particular city or area to live in, some have even opened businesses here. Short of doing something unlawful like stealing other peoples' pokemon, you're generally welcome to do whatever you prefer.