You've probably been and come back... but just in case, we've holidayed in Alikanas several times, and most of the Tavernas are pretty good. Not quite sure what you mean by "proper Greek food" specifically, but there's only a couple of non-Greek-style restaurants. We liked the Lemon Tree, a bit out of the main bit of Alikanas, but quite close, and also the taverna at the eastern end of the main bay (forgotten the name). It's a very small place, and not very lively, which suited us down to the ground. Excellent swimming, shallow warm water but you can swim for a k or so along the beach and back, nice views across to Kefalonia.