Hi Steve,
Just to clarify, the "TransAtlantic Way" (
http://www.transatlanticway.com) is a race in June, starting in Dublin, going to Derry, then using the Wild Atlantic Way (tourist route) as a basis for the rest of the route.
I'm taking it that you're talking about the Wild Atlantic Way (
www.wildatlanticway.com/home/ ).
As an Irishman, I'd tell you to do the whole thing :-) Really it depends what you're in to. The southern coastline will be more rugged, more touristy and more populated. North of Galway can be rugged too, but less touristy and less populated. Of course, depending on the time you have and your inclination, there are plenty of places off route that could be interesting cycling too!
Starting in the south, Kinsale, Clonakilty, Baltimore, Kenmare, Dingle, Ballybunion are all popular tourist spots with some fantastic beaches and excellent food.
Further up, Doolin & Lisdoonvarna are famous for music. And there are the Cliffs of Moher.
Then you have Galway - a fabulous little city full of great pubs and good food.
North of Galway it becomes bleaker but no less beautiful. From here on, tourism is less developed, for some that's a good thing!
I think Donegal put the "Wild" in Wild Atlantic Way. It can be really spectacular!
So, to summarise, if you want the picture-postcard experience, do the southern part. If you want less frills do the northern section (But of course go back to do the other half another time ;-)
Frank