I agree with Frances about Kings Cross (or Potts Point, the area next door) as a good area to stay - or other suburbs in that eastern area - e.g Darlinghurst, Paddington and even Double Bay, Elizabeth Bay or Rose Bay or Rushcutters Bay. However I don't know how well those areas are going to suit your budget.

Not sure when you're visiting Sydney but The Sydney Mardi Gras is a very popular tourist event at this time of year. The main areasaffected are Darlinghurst and environs so accommodation maybe difficult to find until a little time after Saturday 4 March, the date of the Parade (which goes up Oxford St).

Other areas to try for accommodation might be around Sydney University - e.g Glebe, Newtown, Camperdown etc (you need your map for this) or Balmain or Rozelle.

The closer in to the city you are the more difficult the parking problem of course - especially in cheaper places.

Re the Russell at The Rocks as suggested by Barbara - a nice little boutique place I think - I've only seen it from the outside but met someone who stayed there and liked it. Not really in the Budget category though.

Your car will be an advantage if you want to visit any of the National Parks just outside Sydney - Royal NP, Kuringai Chase NP or Blue Mountains NP. Post again if you want more info on specific walks as there are some beautiful ones in all of them. All the New South Wales National Parks are at http://tinyurl.com/lj6zw

Best wishes, Michael Sydney, Australia