Ilike to do sth.

I like to go swiming.
I like to go to swim不是语法有问题，只是老外不这么说。

应该用 I like going swimming.
like doing sth. 固定搭配，喜欢做某事。
go swimming 游泳这种活动。
go to swim 去游泳，表示一种动作。

go swimming是固定搭配，一般不说go to swim

都对。但常用I like to go swimming.

I like to swim

I like swimming

like to do是偶然喜欢做，like doing是经常性的喜欢做
如果楼主想表达经常喜欢游泳，就用后者吧
不过现代英语中对于二者的区分已经几乎不存在了，但如果是写作文或者做题，还是严格按照语法来吧