A first date is like your resume or a job interview. You don't put "FARTS IN ELEVATOR" on your resume or go to a job interview and brag about stealing other peoples lunches. You pay for the first date (assuming you asked her out) because that's the convention, just like you put on a shirt and tie when you interview, even if it's for a job that requires you to wear a nametag.
After a little while, if everything is going okay, you can break into the "cheap dates" phase of the relationship. (Parks, church, Netflix, walks, etc.) In most cases, she'll be as relieved as you are.
Caveat: if you're putting your best foot forward and she's like, "What? This is your best foot?" you may have fatally divergent expectations.
Online dating has short-circuited a lot of this, since by the time you're ready for a first date, you've already seen a person's picture, IM'd/texted, maybe talked on the phone a few times, stalked them on Facebook, found them on LinkedIn, run a background check, and in some cases know how much they make via a public records search. (If they're a public employee.)