To be honest, buses in Adelaide aren’t too bad in the grand scheme of things but, as per the UK, they’re probably the least desirable form of public transport for most people if given the choice. Whilst there is being some work done on giving buses priority at intersections, in peak hour the crawl into the CBD along some of the major arteries (e.g. ANZAC Highway, Port Road etc) can be a bit frustrating.
If you’re going to be truly dependent on public transport then I’d highly recommend finding somewhere along a train or a tram route. It’s worth bearing in mind that on a 40 degree day then your idea of walking distance might be reduced considerably from what you are used to in the UK.
I’ve attached a crude map of the train, tram and O-Bahn lines as they leave the city – I’ve only included a fairly small radius from the CBD at this stage as Google Maps removes most of the suburb name labels if I zoom out any further (rail/o-bahn should be no more than 15 mins from the edge of this map, tram will be 15-25 mins depending on time of day). You should be able to follow the lines out further from here on Google Maps if you are interested in living further afield.
Red is the tram line (the dotted bits are the North Terrace/KWS extensions which will be finished by the end of the year – don’t rely too much on any of the other planned extensions you may read about appearing in the immediate future – especially if the Libs win the state election in March), blue are the rail lines (the Outer Harbor and Grange lines to the north-west, the Gawler line to the north and the Seaford/Tonsley and Belair lines to the south). Google maps should give you some approximate journey times if you plug the start/end destinations into the directions tool. Bear in mind that the trains run largely to schedule any time of the day but the trams will get slower in peak hours as more stops will be required (a peak hour trip into the CBD from Glenelg can take 45 minutes but only 20 minutes off-peak).
The green line is the O-Bahn – Adelaide’s guided busway. Think of it as a train line and not as a bus – it works really well and by the end of the year will feed directly into the heart of the CBD via a tunnel making it even quicker.
As mentioned before, the buses are fine but can be frustrating if they get caught up in traffic and therefore turn up late. You’ll also find that as far as public transport’s concerned, all roads lead to Rome – you can get into or out of the CBD from most suburbs pretty easily, but try going from suburb to suburb and you’ll most likely end up having to change in the CBD, meaning that even short inter-suburb trips can be made painfully long by PT.
With this in mind, North Adelaide would be a great place to live and will give you good access to the CBD by bus, uber or a 15-30 min walk depending on where you start and finish. Croydon is also great – but then I’m biased because I live there. Some of the suburbs along the tram line are also nice – Goodwood, Forestville, Black Forest for example. Glenelg and Glengowrie are safe bets too – but further out. The hills are beautiful and are serviced by the Belair rail line – about 35 mins from the CBD from Blackwood/Glenalta. I’m not sure about the areas in-between Goodwood and the foothills (e.g. Mitcham) – it’s not my neck of the woods so someone else might have to chip in here. Likewise, I’m not sure about the suburbs to the northeast along the O-Bahn, but I’m sure someone else can advise.
Cost of rentals will also vary by area - with North Adelaide being particularly pricey I think. Check out realestate.com.au for some examples.