DON'T take her out for BYOB or bottomless
A few years ago, a guy took me out for sushi on a first date; I hadn't realized it was a BYOB restaurant until he met me at the door with two wine bottles in tow. Now, grammar is admittedly my strong suit over math, but even I knew that added up to each of us finishing our own bottle. Here's how that looked to me: that he was trying to get me really, really drunk. For one, I didn't know him! He could've been a serial brunette strangler for all I knew! (I watch a lot of Law & Order.) It also made me feel like he assumed I wouldn't be interesting enough sober.
Additionally, it made him look cheap. I understand the fiscal argument for paying $25 for two hours of unlimited brunch cocktails, but this is Date One: shouldn't we try to remember if we like each other? Make your date feel like she's worth it to you to splurge on two glasses of the restaurant's best buttery chardonnay. Then, once you're in a stable relationship, you can enjoy bottomless mimosas and all the Three Buck Chuck wine you can carry to the restaurant.