It's a big responsability to suggest you a restaurant for such a day, I think that's why almost nobody answers to you, because a lot of people here knows restaurants.
I think you should have a look some days before to see if you like.
A restaurant more or less in 30 € could be
En Busca del Tiempo
http://www.enbuscadeltiempo.com/index.html One a bit cheaper is Zeraín (Quevedo st.3)
One a little bit more expensive but with very good food is Mesón Gallego II, in Plaza de la Remonta, they have a terraza, and the price will go over 30€ depending on the wine and desserts.
Another good one is Sal Gorda (Beatriz de Bobadilla 9).
You will eat really well in any of this, although I don't find them with the appropriate environment. Maybe Sal Gorda is the smallest one and with a more familiar environment, Mesón Gallego and Zeraín could be a little bit noisy.
To do something special you could like to visit the fiestas de la melonera around the 12th of september (I don't know which day of september you'll come)