I would love to go to Ireland some day as I have some ancestry from there and understand it is quite a beautiful country.
Tolkien did go to Ireland several times and enjoyed the country and the people very much.
However I believe that LOTR is more consciously patterned on the Nordic sagas and mythologies than the Celtic. Some Celtic influence may have been unavoidable in the story since the Celts occupied England before the advent of the Anglo Saxons. It is for the Anglo Saxons, though, that Tolkien was creating a mythology, since he felt it had been repressed by the Normans after they defeated the Anglo Saxons in 1066. I got this from reading Tolkien's letters + a book on him by Shippey, the guy who has Tolkien's post at Oxford now, and who is a great admirer of him.