I'd like to say,"I'll play sports tomorrow." Would dropping the 私は be simpler? So instead, 明日がスポーツを 遊ぶ。as the 'I' can be implied?
As you thought, it seems possible to drop 私は from the sentence. However, the sentence isn’t natural for the following reasons. First, スポーツ isn’t generally collocated with the verb 遊ぶ but with the verb する “to do”. Second, the particle が often indicates subject, so 明日 “tomorrow” shouldn't take it here. Instead, you can simply use 明日 without any particle, because it also has a usage as an adverb.
I'm not sure how much grammar you've studied already.
You'll definitely be understood.
If you've decided in your mind that tomorrow you're going to play some kind of sport, it would be better to state this a bit more explicitly.
As mentioned in the other answer, a more typical verb to choose would be する or やる.