I play magic. If you want to play competitively, go to Rockets on Coursey. They have several pro tour vets that play their regularly. Little Wars is latently hostile to magic players as they are primarily a miniatures venue. As a casual player, Gamer's Paradise in Prarieville is probably your best shot if it's not too far. The pace there is a little slower and a little less cutthroat. For example, I top 4 every time I play at Gamer's Paradise, but I struggle to stay .500 at Rockets.
At Rockets, Standard is on Tuesdays, EDH on Thursdays, and Draft on Fridays.
Gamers Paradise also drafts on Fridays and sometimes on Wednesdays as wells.