Hi Lori,
When we were planning my baby shower brunch, we booked Lindey's in German Village. They have rooms of multiple sizes, a terrace, and a library where you can have your event, and they can even cater the brunch for you too. There is a fee to book the room, but I think it is only $75, fully refundable in case you have to cancel (we know because I ended up in the hospital on bedrest and had to cancel at the last minute). The brunch menu is great - we love the food, and the ambiance is perfect for a shower.
If that is not up your alley, I've also found that if you know someone who lives in a condo/apt. complex and is willing to reserve the complex's community room, you're probably off to a great start! They have kitchens, are easy to decorate, and usually only cost $10 or so (if anything) to reserve.
Good luck with the planning!
C.