LyTeMyCanDyI !!!
I think that I can help you out with this one.
First, If you've decided on Company, it is an excellent choice.
The show is about love, marriage, and dating. And trust me when I tell you that John Doyle's direction works so much better for this show. It's fun to watch, and the performances are just moving, and student rush is front row. Once the front row is sold out they student rush the box seats which I hear are also great. They sell 2 hours before and you can purchase two tickets with one student ID. Tickets are $36.50 I believe( so totally worth it).
If you're still a bit iffy about Company then I also suggest "In the Heights" it's off-broadway but it's still a great show. And a great show for a date. It makes you want to dance. It's really fun and has an inspiring story. Student Rush ticket are $20.00 for front row. The stage is on a bit of an elevated platform so you have to look straight up at times, but there isn't any other obstruction, except for a staircase into the audience cleverly disguised as a subway entrance. The only thing is that this tickets are one per ID so you both have to show up to get seats. A friend and I got there at 4:30pm to get tickets and the box office and cast of the show laughed at us as we waited. So you can show up at around 6:00, perhaps 6:30 and get tickets. If you call ahead at 6:00pm the box office will answer the phone to tell you if rush tickets are left over.
Going to a musical late in its run is like going to a prostitute late in her shift.