Jerwood Gallery in Hastings has a wonderful café with views over the fishing fleet of Hastings and out to sea, so you can eat and watch life going on by the sea shore.
It is an excellent modern art gallery with the collection from the First World War and the 1960s, including works by Barbara Hepworth, Paul Nash, Ben Nicholson, John Piper, Lowry, Walter Sickert and Christopher Wood amongst others. They have two interesting exhibitions on at the end of 2016 on Stanley Spencer and 100 modern artists so there is plenty to see for an hour or so.
A pity you cannot pop in the café without paying for the art gallery each time, but with different exhibitions on there would be different things to see.
There is a small shop as you enter which you can look around without paying. Art Fund members can go in for half price.
On the first Tuesday of each month there is free entry after 4pm, which would be handy if you were local.