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you’ve got 2 pubs in walking distance of the bunkhouse. I’ve not stayed there but it is well signposted.
Up the hill is the George and Dragon. Great views over the Arun flood meadows. Proper beer.
Down the hill is the the bridge inn. No views but I’ve eaten there and it was fine.
For breakfast there is the Riverside Cafe which is over the river on the left from the bunkhouse. It opens at 9 and is cyclist friendly.
And of course you’ve got Amberley station for a bail out option.
Amberley village is a mile or so from the bunkhouse.
There is a bunk barn at half way in Houghton.
https://www.southdownsbunkhouse.co.uk/booking
The pub at Houghton has a good beer garden too and there is also a nice pub in Amberly just up the road.