This is a grammar myth that won't die. More specifically, it's a grammar myth that a billion well-meaning know-it-alls won't let die.
Ending a sentence with a preposition -- something like "She's not someone I would go to the batting cage with" -- is perfectly fine. The sentence is clear, and no one would argue its structure. (Although why you wouldn't go to the batting cage with someone is more of a mystery. What will she do to you?!)
So why do we have this idea that ending a sentence with a preposition makes for an inexpert turn of phrase? It makes sense if you're Julius Caesar but probably doesn't apply to you or me. In Latin, ending a sentence with a preposition really was incorrect. In 1762, an Anglican bishop printed a book of grammar and basically co-opted the Latin rule for English. A good try, but English-speaking peoples had been ending sentences with prepositions for ages, and the practice persisted [source: O'Connor and Kellarman].