Climb back up the cliff route, past the huts water intake, and along the track marked with orange reflective squares to connect with the South Coast Track. Follow this eastwards without difficulty to the Aan bridge, which as of Feb 2022 is "closed" awaiting repairs. Under low flows of the Aan, its a simple task to scramble directly down into the gorge starting right beside the bridge. You can then head down stream to the river mouth to look for DOC markers for a route they've made to the eastern side of the Aan bridge, or about 10-20 metres downstream of the bridge look for a muddy ledge that climbs up the eastern side of the gorge, and push through the ferns to connect with the DOC route a few metres in from the South Coast Track by the bridge.
Continue along the South Coast Track until you hit the unbridged stream west of the Grant Burn. This was upper thigh deep in low flows, probably uncrossable after heavy rain. Cross the bridge over the Grant Burn and then continue along the South Coast track to Waitutu Hut. The last few hundred metres are very over grown and poorly marked, keep and eye out for subtle twists and turns of the track which are easy to miss.
Note: Described in the reverse direction to your journey
The area immediately west of Waitutu is full of dense coastal scrub. The track is poorly marked and fairly over grown for several hundred metres, and if you are coming from the west it can be very easy to miss subtle turns in the track, making for a frustrating experience.
Follow the track westwards. About 10 minutes from Waitutu Hut the track opens up and is easy to follow for the rest of the way to Westies, through a mixture of podocarp and occasional coastal manuka scrub. It follows the old telegraph line to Puysegur Point, the remains of which can still be seen in places.
After about an hour from Waitutu the track drops down between an S-bend of the Grant Burn and crosses a bridge. Shortly after, a second stream is reached (unnamed on the topomap). This stream was upper thigh deep in February 2022 when southern Fiordland was having a drought and Lakes Hauroko and Poteriteri were at least a metre down on their normal depths and the jetboats weren't running on the Wairaurahiri due to how shallow the river was, so this stream has the potential to be un-crossible after rain. There were tree logs in the stream with some rope on the eastern side, but nothing going right across so its a mystery to me how you are supposed to cross it if the water is up!
Once across, the track continues to the Aan River where the bridge is "closed" by DOC (see the DOC website for alert updates). DOC have marked a route south down the Aan to the beach, where you need to cross the river and look for a marker on the true right side, a little bit further east along the beach. Alternatively, under low flows you can walk up the gorge of the Aan and scramble up the bank directly upstream of the bridge. In Feb 2022 the Aan was ankle deep, but again there are warnings about this being uncrossable after heavy rain or high tides on the DOC website.
West of the Aan the track continues, passing inland of where older maps show Westies Hut incorrectly mapped. A short distance past the ravine shown on the topomap (an easy crossing) the well marked turn off to Westies is reached. Follow orange reflector squares through the bush to the top of the cliffs overlooking the western half of Prices Harbour. A roped route heads down around the cliff in a northwest direction to a large square of corrugated iron and pipe which is the water intake for the hut. Plunge down to the west through knee high scrub to approach the eastern end of a massive sea cave. The 2 separate buildings that make up Westies Hut lie inside.
3-5 hours one way.