Couple of places in Dublin:

An Goilin Traditional Singers Club
Teachers' Club,
Parnell Square.
Dublin 1, Ireland
Contact: Antaine O'Farachain
Phone: 085 773 9241
Email: info@goilin.com
Web site: http://www.goilin.com
Begun in 1979, this is the daddy of all Irish singers' sessions. Meets every Friday, September to June at 9:30 PM Irish Time (around 9:45 PM) except the weekend of the Inishowen Festival (see Festivals and Workshops listings) and June Bank Holiday weekend. Cost: 3.00 Euros.

Fingal Singers' Club
Old Town House Pub
Ballyboughal, Co. Dublin
Contact: Dave O' Connor, Ballyboughal, Co. Dublin
Phone: 01 8433691 (or cell phone 087 680 3860)
Email: cllrdoconnor@eircom.net
Ballyboughal (sometimes spelled Ballyboghill) is 8 miles northwest of
Dublin airport. Session meets every Tuesday. Some
instrumental tunes are featured, but primarily good, solid fun singing.

Also - try thesession.org for lists of sessions and events.