First dates should be fun, easy, low pressure, and no more than an hour's time requirement. For those reasons, keep trivia in your back pocket until at the very soonest, the third date. If you have an existing trivia group, don't just show up with a date. Find a new trivia spot to try with just your new honey and wait until things are a little more established until you throw them to your group trivia environment with all your friends.
On the flip side, trivia is a great place to turn a friend into a romantic prospect because people usually go in groups and it's the kind of low-pressure environment someone can bring a coworker or friend who's new in town. This actually worked in my favor once when my girlfriend's buddy from church brought his very handsome and newly single roommate. I flirted my ass off and we ended up dating for a few months. I still praise trivia for metting that killer cutie, and love going to this with my friends.