Right now don't remember where the Avenida Palace is but Barcelona is easy to navigate.
Obviously recommendations depend somewhat on what you are willing to pay.
Michelin star classics like Neichel and La Dama come to mind.
A new place I like a lot is Àgora - la Cuina d'Isabel i Xavier. Modern cuisine with a personal touch. The gratinéed Sea Urchins were particularly good but I am sure you will also find a few things that are less adventurous. Aprox. €30-40 per head depending on the wine.
It is on Calle Sepúlveda. I'll try and locate the card for the exact address and phone number.
Many other great places around but this is my current favourite.