Session is Mondays at Kitty's - doesn't start till 10pm. I think it tends to the militant wing of the ITM movement.
Friday 7 June 2013: Blackboard concert at Mojo Invincible, 161 Willis Street, 7.00-9.00pm Free
Sunday 9 June: Singaround at The Back Paddock, 11-15 Torrens Terrace, 7.30pm (It’s upstairs at the offices of Julie Lamb and Associates, in the D.W. Dentice building. The building is on the left hand side, just up from the corner with Webb St. Look out for the Acoustic Routes sandwich board at the venue entrance.) Entry by koha (collection)
Think that's about it in Wellington. Nelson has lots more but I don't know any details. You could try asking the guys at Ceol Aneas (
http://www.irishmusic.org.nz/ceol-aneas) - quite a few of them seem to be based in Nelson area.
If you're going to the morris thing, David Barnes will know of anything else going on.