Change entrance fees will no doubt keep some people away

no doubt在这里是插入语，意思是‘毫无疑问’。 实际上应该用两个逗号的：
Changing entrance fee will, no doubt, keep some people away.

例句：
He is clever, no doubt, but he is cold, too.

no doubt 是修饰keep的，相当于副词，所以不要用to