Traditional "Downtown" Santa Barbara centers around State and Carrillo streets, which is more the heart of the business, but not necessarily the tourist district.
Where are you staying because there are a lot of restaurant clusters up and down State Street - all of which could be considered "downtown". Love to help you but State Street is so long, and there are lots of nice choices up and down its length, and a few blocks away on either side.
And also agree with prior post - what are your tastes, what are your price ranges, what is your style of dining. There is no one signature restaurant in this heavily restauranted town, but I bet we can come close to something that could work well for you.
Please tell us more.
You didn't give any hints about food types or price range. A lot of the restaurants recommended on this board are downtown.
So here are some of my favorites.
Wine Cask - very nice historic building, excellent california cuisine. (main course $23-$28) 813 Anacapa Street [1 block off state] 805-966-9463 atmosphere is upscale but not too stuffy.
If you want California cuisine but want to spend less try Opal (near the Arlington theater).
Square One is another upscale spot.(but I like wine cask better)
Los Arroyos - [14 W. Figueroa] casual mexican restaurant (order at counter/food delivered), but setting is nicer than your typical counter place, [tile fountain/wood&tile tables/decent flatware.]
El Cazador - an alternative with table service.
SB Shellfish - at the end of the wharf. very casual, not good for large groups. But fun to get the fresh crabs.
Italian - I wouldn't recommend because you can get good italian a lot of places. But if you are in the mood either CaDario or Olio Limone.
The Palace - if you are looking for a really fun spot with okay cajun food.