Through Canberra and across to Batemans Bay via the Kings Highway is probably the quickest but there are a lot of bends and twists up hills and down hills with a big decline on the Batemans Bay side. You have the rig so drive according to conditions. Trucks do it all day and night.
You could also go Canberra to Cooma via Monaro Hwy, easy run on the Monaro. Then across to Bega, then Tathra. Still twists and turns.
The longer way but easy peasy, down to Benalla then head across to Yarra Glen, Co ckatoo etc then come out at Pakenham then an easy drive along Hwy1 to Tathra.
As I said, you have the rig so just drive to conditions and enjoy. Tathra is a lovely place.
Keep Safe on the roads and out there.
__________________
Live Life On Your Terms
DOUGChief One Feather (Losing feathers with age)
TUG.......2014 Holden LT Colorado Twin Cab Ute with Canopy
DEN....... 2014 "Chief" Arrow CV (with some changes)
You could also go Canberra to Cooma via Monaro Hwy, easy run on the Monaro. Then across to Bega, then Tathra. Still twists and turns.
Keep Safe on the roads and out there.
This is the easiest, and shortest way. You will have one big twisty hill to tackle ,Brown Mountain, but otherwise it's an easy run with a big van. Trucks follow this route daily.
If the brown worries you you can go Canberra, Cooma, Bombala, Pambula, Merimbula or Bega and then to Tathra.
To get to the coast, you have to go down a steep mountain road for a few km. Once down, the rest is easy. DO NOT rely solely on your brakes - use low gear. The Kings Highway probably has a shorter length of downhill, but I reckon it is steeper than Brown Mountain. There is a lot more ACT traffic as well. I recommend to go through Cooma and then down Brown Mountain. You an expect a fair bit of traffic on either road at weekends.
To get from Wagga, you have 2 choices - come over the Snowy Mountains, or go through Canberra. At this time of the year, no contest - Canberra, because of the risk of snow and ice on the Snowy Mtns road. In summer, I would choose the Snowy Mtns, but there is one very steep climb coming up from Talbingo. I used to tow my 16.5 ft Jayco with a 3.2L diesel Pajero up there in 3rd gear (manual transmission), but it is steep and narrow winding road. After that climb, easy run for the rest of the trip.
Timewise, the Cooma route would be quiker, because the Princes Highway is a bit of a goat track, and you have a few towns to go through whereas the Monaro Highway/Snowy Mtns Hwy is generally more open country. Going via Canberra, Cooma to Tathra will take you about 4 hrs driving time, whereas via the Kings Hwy and Batemans Bay will take you about an hour longer. People seem to have a phobia about the Brown Mountain, but if you take your time, use the engine and gears to brake as well as the brakes, it is an easy and safe drive. Milk tankers and other trucks use the Brown every day. It is only 10 km of steep, winding road. Hell, I have even ridden my bicycle down and up it!
I do much of this trip every few weeks as we have a holiday house down near Tathra. Erads response above is spot on with what I'd recommend.
Just be aware that there is a set of temporary traffic lights on the Brown Mountain road as there is a short section where one lane is closed due to some damage. I'd still take this road instead of the Clyde Mountain, as the Clyde has more traffic and is a rat race of aggressive Canberra drivers.
At this time of year you'll also encounter a bit of ski traffic between Canberra and Cooma, more so between Friday afternoons and Monday mornings.