The Hanuman Restaurant 93 Mitchell Street in Darwin's CBD is a must visit and specialises in Thai, Indian & Nonya cuisine. They do a thai crispy whole fish with a 3 flavoured sauce. Here's a link to the menu. http://hanuman.com.au/
http://gravitydesignwebsites.com/wp-...-menu-2016.pdf

Char Restaurant 70 The Esplanade Darwin despite being famous for their steak also have seafood on the menu. The link to their website is down at the moment but they also have a Facebook page with links to the menu [MENTION=765892]charre[/MENTION]staurantdarwin althought it's at the pricey end of the scale. http://www.chardarwin.com.au

There are also some recommendations from the Qantas Travel Insider blog.
Darwin?s 9 Best Restaurants | Qantas Travel Insider

I lived in Darwin from Dec 2000 to Feb 2011 and really enjoyed my time there. If you're looking for something super casual just head down to the Stokes Hill Wharf (at the end of Smith St) where there are a number of eateries. There is also a bottle shop (Aussie vernacular for liquor store) selling beer, wine etc. Our favourite was getting some pad thai noodles from Siam Thai on the Wharf. If you're going "soon" I'm guessing that is before April so the Mindil Beach Sunset Markets won't be on then as they only operate in the dry season April to October on Thu & Sun evenings.

Parap Village Markets are on every Saturday morning so it's a great place to head to for local produce and many different kinds of Asian street food. You can get Darwinbus public transport from the City to Parap which is only about 5 minutes from the CBD.