Buy the Sussex and Surrey pub of the year whilst you're in town: http://www.worthingherald.co.uk/news/couple-put-award-winning-worthing-micropub-on-the-market-1-7739972
Worthing has a newish burger joint which is getting favourable reviews. I've yet to visit myself to try their veggie offering.
http://www.thewoodsburgerkitchen.com