For orientation,
this map list all the hotels and restaurants
Below is my opinion only - I am not a "foodie" but enjoy good food at good value in a fun atmosphere.
Except for Azteca 2 (good Mexican food) next door inside a holiday resort, nothing else within easy walking distance of the Hilton.
The Hilton has a nice tiki bar - but a tad bit expensive for locals who get similar drinks for much cheaper elsewhere - and the hotel food/restaurant is quite good.
Assuming you have a vehicle, the nearest best restaurant is Florida's Fresh Grill (do make a reservation - it is popular and deserving of its great reviews). Branos (Italian) a bit further north is also very good.
However, to join the locals and visiting crowds, you need to drive to one of several restaurant "clusters".
To the south, you will find the Coconuts-on-the-Beach "cluster" with several restaurants - Coconuts is fun, right on the water with live music and inside/outside bars/dining. Fat Kahuna's is in the next block west - a bit expensive but different.
At sunset on a nice day, many locals head to the Ron Jon "cluster". They either visit the Sandbar near the beach or go west to watch the sunset from Sunset Waterfront to the music of "time to say goodbye!". You can then go to dinner next door at Florida's Seafood - always popular.
Locals also flock to the Cocoa Beach Pier "cluster" to watch sunset from the tiki bar at the end of the pier. Dinner at the pier is fine with ocean views. For something different, Barcelona Tapas near Publix serves good Mediterranean food.
Finally, most visitors drive to the Cove "cluster" at the Port for typical Florida beach food. The cruise ships depart around 4pm and sail right in front of the diners! Grills is a good starting point but Rusty's and Fishlips are just as good. Millikens has the best tiki bar with white sand!
Later in the evening you may want to have drinks at Preacher Bar next to the Radisson for a classy yet different experience.
Choices, choices! Have fun!
