Fast travel to Badtown, in order to save time. Once you are there, enter the city area and go to the marked bar. Inside sit at the table, wait for the game to finish, get up and leave.
Follow the man in white suit, but do not let yourself be seen. Each time, before he looks behind, the man will stop. It's a visible sign that you need to take cover. If you lose sight of your target, you will have 20 seconds to find him again.
Finally, the man will enter the building shown in the screenshot, which will finish this mission.