Hi Solanum,
I live the southern part of Adelaide. There is a lot you can see even in the city - double stars, planets,moon that are completely unaffected by light pollution.
If you are living in the outer fringes then many of the brighter DSO are visible as well, though not as nice as in dark skies.
If you have a bit more aperture (like my 16") then the narrowband UHC and OIII filters work really well to bring out nebulae , which make up almost half the interesting objects in the skies. Don't waste your time with a general light pollution filter as they will make a subtle difference on emission nebulae only. Also, the larger the aperture,the better the narrowband filters will work, especially with the OIII.
For galaxies and fainter clusters you will need to get out of Adelaide I'm afraid, but the good thing about Adelaide is that you don't need to drive too far to get pretty dark skies.
When at home, I tend to use my ETX 125 mostly and view the moon,planets, doubles etc - but can also see many of the main DSO's like the Swan, Orion, Globs and Open Clusters. If I use the 16" I can still see much more detail than the 5", and the UHC/OIII filters in the big scope bring out emission nebula like nothing else. I have a Moon and Skyglow filter but don't use it as the difference it makes is minimal.
Once or twice a month, I usually travel 40 mins to Tooperang or 60 mins to Stockport for an ASSA viewing night in dark skies. The 3/4 of the sky away from Adelaide is just about as dark as anywhere else. I usually spend most of my time hunting down faint fuzzies I can't see from home.
So there is still plenty to see if you move to Adelaide!