You can "game" anywhere. As long as you are in a relationship the socially acceptable way is to just "have a beer with your friends". It may be inappropriate to go to clubs, so you have to stick with pubs and other venues.
The good thing about relationships while gaming is that you are forced into the right attitude, the optimal attitude of pickup. You cannot approach for the sake of pickup anymore, which is good (since that removes your agenda). Instead, you have to learn how to just mingle around, be open and social without expecting any outcome. This in turn will teach you how to approach without risk of rejection, how to stay under the radar. It is perfect! So stay in that relationship as long as you can until you have mastered the game.
Have no expectations. I find when I used to roll into a place with the intentions of just macking hard on girls that it never turned out in my favor. But if I went in, was just having a good time with my boys that the convos with cute girls just flowed.