Aero,
Saturday's & Wednesday's NT News are the best for accom. Plenty of share accom usually. I think around $100/wk or up would be average, but having been out of the market for some years I could be leading you up the proverbial.
Mrs Claret has a 1BR, airconditioned unit, a 5minute walk from the Smith St Mall (CBD centre), on The Esplanade, 5 minute crawl from Lizzards (Bar & Grill), just off the pub/cafe strip (Mitchell St). Fridge & washing machine provided. Can provide basic kitchen utensils and crockery.
Not sure what rent she's asking but between $160 & $180 at a guess.