First, try to position all M&G's for mid-afternoon drinks. Preferably coffee or tea, fruit smoothies, etc. That avoids the dinner dilemma, and you can still decide to go for food if you want to. If she's really nervous about meeting you, the lack of booze may help her feel comfortable you are not trying to get her drunk (or drugged). If she's already DTF, and she's a noted drinker, or you share an interest in wine/beer/booze, etc., then a bar makes sense.
Next, if you want to take her to dinner as part of a date, my advice is to pick a place YOU like and can afford. Make sure to find out if she likes or dislikes the food there. My #1 hates fish. Just HATES it. So no sushi, no Water Grill, no Roy's for her. I recommend you only go to that $$$-$$$$ place because you feel like a treat. Will she be impressed at a $800 dinner check for 2? Yes - for about 10 minutes after you leave. Then she's going to wonder why you didn't take her to Denny's and give her the extra $750. One more consideration: ask her what her favorite food or restaurant is. Then Daddy can please his Baby well, and it often won't be very expensive.
It's important to think about cash vs. stuff the way an SB does. You can spend thousands on her (and you) for food, travel, clothes, etc. and she will appreciate it. But once you drop her cash allowance in her hand, she forgets anything that doesn't end up in her wallet or closet. She will be driving home from your date wondering how soon she can get more cash from you, then she'll burp form that $65 Ribeye steak and that $270 bottle of Jordan Cabernet and start wondering about getting more cash from you again.
You're off to a good start. Enjoy your adventures in the Sugar Bowl.
Life is good
The Cat