Golf, tennis, rugby, football, innebandy, sailing, beading, art classes, you name it, it is probably available in Accra. If you are sporty, the climate may take some time getting used to, and depending on your heat tolerance you may consider exercising in the early morning or later in the afternoon when you first arrive. If you are on facebook it might be useful to join the following groups - Ghana Expat or Expats in Accra to get a better sense of the expat community in Ghana.
For children there are multiple activities available including ballet lessons, drumming, African dance, horse riding, tae kwondo. If you or your child wants to learn something then somebody somewhere will teach you.
You may like to spend your weekend at the pool of a local hotel. You pay to swim and the charge covers sun lounger and sometimes a towel. Alternatively there are a number of beach resorts within an hour or so of Accra. Take care in the water. Rip tides do occur. If you are not a confident swimmer, check if there is a lifeguard available or look for a competent local who is familiar/comfortable with the water and pay them to stand guard.