Being a northerner who's recently moved south, I'd recommend (in addition to the excellent suggestions already) - taking in the Large and Small Magellanic clouds under a dark sky, nebulae and clusters in Sagittarius / Scorpius area, and a good bit of time exploring Eta Carinae, Crux/Centaurus and its surrounding area. In the north, we're spoilt for galaxies, but clusters and diffuse nebulae, not so much. And there's nothing like the LMC and SMC!
Taking a few evenings with binoculars and a small telescope, and some of
the charts here, you can have a lot of fun exploring the Magellanic Clouds - quite a tangle of nebulae and clusters and star clouds. From a dark site, even with the naked eye or binoculars they are a wonderful sight (best in spring/summer, but also visible at other times) with lots of individual nebulae and clusters visible.There's also the 47 Tucanae globular nearby.
In the Sagittarius/Scorpius area, don't miss open clusters NGC6231, M6 and M7, nebulae M8, M20, M16, M17, globular clusters M22, M4, NGC6397, NGC6541, and of course the glorious star clouds near the centre of the Galaxy (all best in autumn to early spring).
In the Carina area, you could spend ages exploring the Eta Carinae nebula, especially from a dark site, and the gorgeous clusters NGC3293, NGC3532, NGC3766, also the Southern Pleiades . Also check out Omega Centauri, Centaurus A and M83. (all best in late spring to autumn)
There's something new for all seasons in the southern sky, so whenever you're down I'm sure you'll have fun!