Just being pedantic, but the president actually doesn't have the power to create national parks - only Congress can. The president can create national monuments, though, which are pretty similar for all intents and purposes.
Just to be pedantic: in The West Wing, season 1, episode 8, this is a key plot point. According to this episode, the Antiquities Act does give the president this power.
Since this is a really silly but rewarding conclusion to the episode, I'm going to have to disagree with you on this.
The Antiquities Act of 1906 does not give the President power to declare National Parks; only National Monuments [1]. This is a mistake in that episode, and the link you cite also mentions this (see the "Trivia" section).
