The Felix puts you so close to so many good restaurants - we use it a lot for our business guests who all enjoy the hotel a lot.
We don't do a lot of steak dinners so I'll leave those suggestions to others except to mention Epic on Hubbard where I had a genuinely wonderful steak shortly after they opened. They have a nice rooftop cocktail space which is quite lively after 5PM but a very soothing spot for a late afternoon drink.
But don't limit yourself - a short walk down Clark brings you to the Bayless empire - and lunch or breakfast at XOCO is great (the aztec hot chocolate alone is worth the trip) - and if you enjoy "new american" as well, try Naha which always makes us happy. Our office team also enjoys Mercadito for a varied taco menu and lots of salsas.