I don't know if they're the best but here are a few fun and not too difficult ones that you can probably find the abc notations for at
The Fiddler's Companion -

Angeline the Baker
Boys From Bluehill
Liza Jane
Kesh Jig
Eighth of January
Ashokhan Farewell
Campbell's Farewell to Red Gap
Sail Away Ladies
Red Haired Boy
Harvest Home

Slowplayers.org is another good online source for Irish tunes, most with abc's and sound samples.

In print, the Fiddler's Fakebook is a good source. It contains about 250 arrangements of mostly well-known tunes from both sides of the Atlantic.