I went there a few years ago. Sitting in the open, on the seafront, staring out to sea with a cup of tea was a really lovely, and quite British, way to start Xmas day. What topped it all was when Santa whizzed past on a Wetbike.
Hello mate. The cafe at/near the peace memorial on Hove lawns has been open on Xmas morning in the past as I've used it myself. I can't remember the name but it's not The Meeting Place...it's the other one. Although this is not to say The Meeting Place isn't open as well. Give them a call.