I chose to rent one of the pavilions at O.P. Schnabel for my baby shower in March. It was $100 for 4 hours for the smaller one. That's the weekend price. I think it's a little cheaper during the week.
Brackenridge is nice. That's where I originally wanted to go but I doubt you'll be able to rent anything there on such short notice. When my mom called, they told her the pavilions there are usually booked 6-8 months in advance.