Always pay on the first date. You never know whether or not you'll run into someone that knows her (read: don't risk getting a bad reputation for being cheap). This way, you can tell pretty quickly if she's a leech or worth keeping/pursuing.
This is the equivalent of betting out early (in poker) with 5 callers behind you just to see where you stand.. and where they stand.
At the same time, if she's someone worth pursuing, don't be the eediot that takes the first date to the "dollar menu" or a place that will run your tab anywhere close to the three digit mark. Very bad to set expectations high from the start...