The Elgin Winter Garden theatre is a fancy venue akin to the Royal Alexandria or the Princess of Wales. The Elgin is used for big stage productions like the musical Wicked. Right now, there's a show based on Cinderlla (being touted as a "sillylicious family musical", that'll be on until early January.
Inside, the place is excellent. Every seat is comfortable, but some of the higher up seats get really far away. I would recommend trying to get seats as close to the front of the balcony as you can, because it's an excellent vantage point.
Dress code is usually defined by the show you're seeing, but even then nothing is mandatory. I've seen people wearing expensive suits sitting next to a kid in jeans and hoodie.