I came out to Australia on my own back in the 90's on a working holiday visa and was here for just over a year and had a great time. I didn't find being on my own a problem and enjoyed the experience. In fact, I enjoyed my time here so much I emigrated with my OH 10 years later to Adelaide.
We are a similar age to yourself with no children. When we arrived after an initial 2 week stay at temporary accommodation, we rented in Goodwood. We didn't really know any of the suburbs, just some to avoid! We went to look at an apartment in the city and the real estate agent said to us "I have the perfect place for you" and told us to meet her there the next day and showed us the unit in Goodwood (which was furnished as well, which we were looking for as we sold up our property and contents before we came and just brought out our suitcases mainly full of clothes!). We didn't have any idea about the suburb, but it was close to the city and OH could catch the tram into the city where he had secured a job and I could take the car to my job so we didn't need to buy a second car, it was close to the shops, we only had to sign a 6 month lease (often they are 12 months) and we got a good 'feel' for the area so we rented it!
When we were looking to buy a house, we looked at many areas, but ended up buying a house around the same area. If you look around the Unley area and the surrounding suburbs there are some good areas. We find it a safe, friendly area. There are plenty of coffee shops and restaurants around, we can drive into the city within 10-15 minutes, have access to buses, trains and the tram and drive to a variety of beaches within 15-20 minutes, we are close to the airport and when we go away we just catch a taxi to the airport and it only costs around $20. I used to work in the South and I didn't have an issue driving South as I was going the opposite way to the traffic. In fact, I have worked all over Adelaide and I find it is a pretty useful starting point to go in any direction for work and I usually find I am going in the opposite direction to the heavy traffic.
Of course what is suitable for one person, might not be right for another, it is all down to personal preference.