Astronomy is pretty cool :) Yeah, the H-R diagram plots luminosity vs. temperature (decreasing), so the biggest, brightest stars are at the top left and the smallest and dimmest at the bottom right with the red giants hanging out in the upper right corner. Most stars (the main sequence) can be found along the diagonal from top left to bottom right.

To talk astronomy on a first date, I might suggest asking about a favorite constellation and then pointing out some of its neighbors in the sky and some of the more prominent stars.

You can have some fun with Orion, for example. Find Orion's belt and follow it down and to the left until you get to a bright blue star. That's Sirius, and the constellation is Canis Major, Orion's hunting dog. From Orion's belt again, follow it up and to the right until you come to a red star at one tip of what looks like a "V" shape. That V is the face of Taurus the bull, and the red star is Aldebaran. Following the line of Orion's shoulders up and to the left you'll come to three stars in an elongated 'V'. That's Gemini, the twins, the two stars at the top are Castor and Pollux. Pollux is the brighter one, on the left. And Castor looks like a single star, but is actually six binary pairs!

If your date things that's cool, maybe one day you can talk to them about the different fusion reactions that occur in the core of a star, but I wouldn't lead with that. :D

They are usually seen when closing bank account.