The only mistake you made is that you said ために instead of ための. The correct sentence is:
それのための場所がありません。
ために is adverbial (modifies a verb) and ための is adjectival (modifies a noun). Obviously you want それのため to modify 場所 (noun) right after it, so you should use の.
See:
In addition, それのため is a bit wordy; you can simply say そのため.
そのための場所がありません。
P.S. You don't have to apologize for making a wrong sentence, but we don't do general proofreading. Next time please specify the grammatical point you are most concerned about.