Dining at the chef's counter is a great experience! In fact, I just made a reservation last night for my Memorial Day weekend vacation. You'll feel like a judge on a fine-dining cooking show.
You can order off of the regular menu, but it's a lot more fun just to turn yourself over to the chef. You'll be asked if you have any dislikes, food sensitivities, etc., and then you'll be rewarded with a great multicourse meal. If there are specific dishes on the menu that you want to try, feel free to ask that they be included.
One of the best parts is that you and your daughter will be served different dishes. In order to get a taste of everything, I like to eat half of each dish and then switch plates with my dining companion.
They will also do a wine pairing, with different wines for each course. I think it's around $50 or so extra; however, if you're feeling really extravagant you could ask if they'll do an upgraded pairing. They've done it for me a few times. I don't recall what I paid, but it was less than I expected.
NR has far and away the best food in the immediate area (this is based on MANY meals there) and pretty near the top of all Orange County restaurants.
I don't know what you meant about any "warnings," but I will say this: Despite the cost, the ambiance is fairly casual and it can be loud. If you're looking for a fancy, quiet meal (like at a Michelin 2- or 3-star place), then NR may not fit the bill. But if you want a fun and interactive experience, you should be thrilled.
Be sure to share your experience with us!