Opera being my "specialty," I can recommend some things.
If you want something with beautiful music and high drama a la Bohème, I suggets you go see the Cav/Pag (Cavelleria Rusticana/Pagliacci) double bill they do. Both are one act operas that are only about 75-80 minutes long. Pagliacci has one of the most famous arias ever, Vesti la giubba, which I'ms ure you'll recognize as many commercials and movies have used it.
If you're looking for an opera that's very serious, but I think has some of the most beautiful music ever, I would suggest Eugene Onegin. It's Tchaikovsky at his best. The only downside is that it's in Russian, which might turn off someone, but it shouldn't be a problem. This one's around 3 hours as well.
If you're looking for a light comedy with enjoyable, but not exactly beautiful, music, go for L'elisir d'amore. I would equate it to Hairspray. The music isn't beautiful (save for una furtiva lagrima), but it's not meant to be. However, the music is a lot fun, and you'll definitely laugh. it's about the length of a broadway show too...2 1/2 hours. Same goes for La Cenerentola, which is the Cinderella story (not Disney's though). It's Rossini which means great music, and a guaranteed laugh. This one is about 3 hours.
Lucia I would suggest because it's obviously a very famous opera, but also because Anna Netrebko is singing, and she is definitely someone you want to see.
Anymore questions, just ask.
-There's the muddle in the middle. There's the puddle where the poodle did the piddle."