Aktur Park is a funfair in the heart of the city and has a range of rides and attractions on a medium sized location, plenty to keep the kids (and young at heart) entertained for a few hours.
With all the traditional stalls, candy floss (cotton candy for our USA friends) and toffee apples etc, some sideshows in the style of "hit the target to win" and there are some well maintained large amusement rides including a small roller-coaster, pirate boats, go-karts and dodgem cars etc. a good mix of rides suitable for all ages.
Like most parks like this its most atmospheric in the evenings and night, not to mention it's probably too hot to visit in the daytime anyway.
http://antalyacentral.com/attractions/aktur-park-funfair