At the moment you are following English sentence patterns. Putting the noun at the end is more Chinese. 我去过很多次北京/我打过很多次篮球, or perhaps slightly more common 我打过好几次篮球. Same meaning. It’s also possible to place the noun at the beginning for emphasis. 北京我去过很多次/好几次. You may also find 了 at the end of these sentences sometimes just to show it has been many times “up till now”. Doesn’t really change the meaning, but Chinese often like to drop a 了 on things, so don’t be afraid when you see that.