Near St. Andrews
You may have already visited but I've only just seen your question. I live fairly nearby and know them both (I eat out a lot, both at home and away). Lathones used to be fantastic and I had a great tasting menu there a few years back (as well as other meals at other times). However, I last went about a year ago and it was gone seriously downhill. It's like they've downscaled their menu as well as down 'classing' it if there's such an expression?! The music they have there is great and if you just want to have a bite before/after listening to that, then great but I think they now seem to be concentrating on their music rather than food.
The Peat Inn is another story. It's lovely and I visit on a fairly regular basis. I was worried when the old owner sold up a few years back but the new owner has probably improved it (so much so that I think, I may be wrong, that they've just won a Michelin star?? ).
If you're on a budget and you're happy with no choice, then go for their set lunch menu. Three courses (no choice) for something silly like £20/head - it's always scrummy. The one complaint I do have is that it's always freezing in there and I'm talking about before this cold Scottish winter too so wear a sweater!