After plugging in all the numbers into my spreadsheet for a similar trip (pick up at airport, drop off somewhere else) the winner was Budget. Budget has a location just off William St. in Kings Cross within walking distance of Hyde Park. (My four year-old daughter and I walked to Hyde Park then took the subway one stop to Circular Quay.)
I highly recommend Budget. Our booking had us returning the car in Wollongong. While there, we decided to hold onto the car for an extra day and return it in Sydney. As we arrived in Sydney we hit yet another really bad storm (theme of our trip), so we were forced to return the car the following day, now two days later than originally booked. To our surprise, we ended up being charged the weekly rate, so it wasn't as expensive as we expected. (In contrast to Alamo, which will use any excuse to charge excessive penalties and extra fees.)