i go to broadway shows with my girl all the time and we always try to dress appropriately. I've seen dudes with hoodys and baggy jeans or shorts....really not classy, although there is no dress code.
Book of Mormon is the top broadway show as of right now. Getting affordable tickets is another question. They tried selling me front mezz tickets for a show in January of 2012.
There ARE deals out there that you will have to look for. You can def get some sick discounts for tickets....I got $70 tickets for catch me if you can for rear orchestra seats. Also keep in mind that popular shows like Wicked and Book of Mormon never goes on sale for cheap, since these shows are mostly sold out. I bought mid mezz seats for November show of Wicked, right in the center. Cost me about $130 per ticket.
Whenever my girl and I hit the city to watch a musical, we always have dinner first and then go bar hop afterwards!