The sentence that is punctuated correctly is:
"For my birthday I received a new bike that I plan to use in a race next month and a gift card to the local book store."
However, it would be even clearer with a comma after "birthday":
"For my birthday, I received a new bike that I plan to use in a race next month and a gift card to the local bookstore."
As for the second sentence, it should end with a period for it to be complete:
"The club can meet in one of these locations."
Additionally, "book store" should ideally be one word: "bookstore."