At the KV end you have basically three choices.
1. Up the Hume hwy, then right at the Sutton Forest servos then through Exeter (turn left after you go under the railway bridge, and right to avoid moss vale). This will bring you into KV from the west.
2. Up the coast. The Prince's hwy up from Bateman's Bay, Ulladulla etc. then turn left at Bomaderry and up to KV.
3. The link road from either Braidwood or Tarago, and through Nerriga to come out near HMAS Albatross at Nowra, then zip over to Bomaderry and same as option 2. A bit of good quality fast dirt 3k via Tarago, or more like 20k via Braidwood.
There are a couple of other more interesting routes into the valley, but if you are towing you will find the main road interesting enough from either end.
I love the stone formations on the link road, but the coast may be worth checking out if you have never been up that way. You could go up one way and back another. There are a mile of places to stay on the coast. Or you could come up Snowball Rd from Cooma to Braidwood and then follow the link road.
Timing wise, we do Canberra to Bomaderry via either Exeter or the link road in about two and a half hours.
