Should I apply to NYU?

I'm not sure. I want to apply to five schools. Baylor University, PSU, TSU and U of H. I want to apply to NYU as well, but I don't think I'll get in. My GPA sucks it's 2.8. I was lazy freshman and sopre year, but I pulled myself together junior year. I got a 2030 on my SATs. I've been in a lot of clubs. I've done some volunteer work. I'm in 3 AP cles this year. AP Gov. AP Euro and AP Psych. My mom says I should just apply because you never know.