I like the idea of doing it during dinner, as others have suggested, but if you really want to make it a big deal in public, I still think doing it during one of the shows would be great.
As for the promise ring, call me old fashion or perhaps an idealist, but my personal feeling on the matter is don't do it. Take it from an old romantic when I say she will absolutely love anything you put on her finger. My best advice is to go shopping for a ring. Take a friend with you if you want a second opinion. But shop around and look at all the options available, and then select what you feel in your heart is the right one. And trust me when I say it'll be the right one.
When my son came to me and said he wanted to propose to his girlfriend of many years, I couldn't have been happier and more excited for him. He kind of felt the same way you do about the ring. He went shopping for rings and wasn't sure what to do. As another option, my wife and I showed him his great-grandmother's ring. It was a simple white gold ring with one 3/4 carat diamond in the middle with 4 small diamonds on either side going down the ring. It didn't look really nice, but I told him he could get it cleaned, polished, and have one of the diamonds that was chipped replaced. He decided to give it a try and when we got it back from the jewelers, it looked brand new and was absolutely beautiful. She loved it! And when she found out it belonged to his great-grandmother (who died when she was 103!), his fiance loved it even more because it was not only a ring, but it was something very special to the whole family.
Keep in mind it doesn't have to be traditional, unless that's what you want. It could be yellow gold, white gold, platinum, etc. It could be a diamond, ruby, emerald, etc. Don't listen to what others want you to give - give what you want to give.
And while others may disagree with me, a promise ring is not for a such an occasion. Give her an engagement ring - something from your heart, and she'll love it forever.