C.J.
Call some actual restaurants. For example, Blue Mesa only charges $50 for a room (on weekends only, weekdays it is free) because they make their money off the food. If you do a buffet with a variety of appetizers it can be about $12 per person with non-alcoholic beverages.
So, call a few places that have party rooms and see what you can work out. Maybe a minimum food purchase would equal a free room or extremely discounted room price. Some places that are pretty neat, but not sure about the rooms:
Brewed on Magnolia, Live Oak (we had a huge dinner for my friend there and they let us eat in the performance area since no band was playing), Blue Mesa on University, MiCocina, and Central Market (they have that big patio area and depending on weather could be a LOT of fun and affordable since you can purchase food/drinks inside and simply walk it out and serve:)
Have fun!!
FYI: Not really sure what your budget is, but you mention a $350 price point. I really don't think that is realistic. I have never seen anything for less than $8 a person and the reality is after drinks and 3 -5 pieces per person (appetizers) the average cost is more like $15 a person.