下周跟我去游泳怎么样? 英文

How about going swimming with me next week?
go swimming 是固定搭配，不用go to swim

how about going to swimming with me next week ?这个要用在，如果对方问你我们明天去哪里，那你就能回答，how about....
如果你直接问她/他要不要去游泳就问，you want go swimming with me next week ?
one is sugguestion , one is question , you go and think abpout it youself
my answer is not perfect but just type what i'm thinking about your question

How about swimming with me next week？

going to swimming with me next week is all right?