"I want to go swimming tomorrow evening."
Just the difference between "want to go swimming" and "want to swim", no substantial difference.
Not anywhere, not at the end - it's just verbally weird when placed at the end.
In English there is a difference in emphasis depending on where you put the time word. "I want to go swimming tomorrow" reflects that the swimming may happen tomorrow but the wanting happens now. Is that something that can be expressed in Chinese?
Do you mean the wanting happens in the future?
I think in Chinese it can be said literally, such as 我明天晚上想去游泳, but the literal meaning is as strange as I will want to go swimming tomorrow evening. Usually that would be interpreted as wanting now too, although arguably not the correct syntax.