A client just reminded me of this... You can't bring dogs into the square or in to the space at Harrahs.
Cabrini Dog Park is @ Barracks & Dauphine (off leash) and can be a great place to play... It is not a members park so anyone is welcome. It can get a little "interesting" so you may want to observe before you let your baby in to play.
Chiwawa Gaga is a great little pet store @ 511 Dumaine Street.
Pirates Alley Cafe is a fantastic dog friendly restaurant located @ 622 Pirates Alley - next door to St. Louis Cathedral.
Have a great time! Mine two are staying home (to loud, huge crowd makes me nervous!)... Mommy is going to play!