There's a restaurant business in Galway selling 'Ard Bia' - ard means high (as well as a whole host of other things, I might add) and bia of course means food, but what do they mean by 'Ard Bia' ?

Ard in Ard Bia is a noun: height, top (as an adjective it would be Bia Ard or Ardbhia, Ard-Bhia with lenition)

So, it is: Height of Food.

Maybe "Haute Cuisine"?

It's definitely Ard Bia without the slightest mutation - once again they're using a name in Irish and the rest is in English - perhaps using Irish names is considered useful as a marketing ploy, it might even have become even more chic and upmarket than French - (Oh là là!
www.ardbia.com

Would it be more idiomatic if they used something like a summit of pinnacle rather than just "ard"?

_________________
A language belongs to its native speakers, and when you speak it, you are a guest in their homes.
If you are not a good guest, you have no right to complain about receiving poor hospitality.

And this would be easy to fix by just putting a punctum delens over the B. They wouldn't have to change their web site's domain name, really. Though I would also purchase ardbhia.com if I were the proprietor.

He's sent me an explanation - originally it was called Ardara Food, and they've changed it to Ard Bia. He knows that it means 'high food', but it still doesn't make very much of sense to me - either way, whether it's in Irish or English.