Having lived here for more than 30 years (orig Lancashire) I havent used the accomodation - but having taken a look at a few around the CBD, other visitors reviews and location I reckon the Country Comfort Adelaide - "The hotel is located on South Terrace, overlooking Adelaide parklands and the picturesque hills beyond. The Adelaide Central Markets are a short walk from Country Comfort Adelaide. The hotel is situated on the fringe of the city centre and is an easy 10-15 minute walk to popular shopping and dining precincts "- the Tramline is very close by that will take you directly to the city or down to the seaside suburb of Glenelg (gr8 day trip) - having said that you may find accomodation in outer suburbs cheaper although you will need to use public transport.
Whilst in Adelaide - visit Adelaide Zoo currently exhibiting the only Pandas outside of China, Glenelg, Victor Harbour and regions around this area, Barossa/McClaren Vale wine regions, Botanic Gardens, Adel Hills - Warrawong Sanctuary and if you can afford the trip and a few days Kangaroo Island.
Hope this is helpful and you enjoy our city. about 10 years ago