There is hardly anywhere in Ireland that you couldn't find some association with St. Patrick or a place named for him. But here are some of the most important: 

Lough Derg (Red Lake) Co. Donegal.
This island contains a shrine to Saint Patrick. Legend says he killed the lake monster there and its blood dyed the water red. Many people go there on three-day pilgrimages to pray from the first of June to the 15th of August. Lough Derg is said to be a cure for the seven deadly sins.

Saint Patrick's Isle Located at the Isle of Man, just off the coast of Ireland, this island is where Saint Patrick is said to have brought Christianity to the people there. 

Downpatrick Shrine Downpatrick, Northern Ireland.
The Cathedral Church of the Holy Trinity (originally named Church of Dendalethglass) is where Saint Patrick, Saint Brigid, and Saint Columba are believed to be buried. A bell, tooth, and hand from Saint Patrick were discovered in the 12th century. Saint Patrick's hand was enshrined in silver and placed in the high altar of the Abbey Church. Water was poured through it to heal sores. The bell and tooth are in the National Museum of Dublin.

Glastonbury Shrine
Relics from Patrick the Older, believed by many to be Saint Patrick are housed at this English church. A translation feast is held on August 24th.

Sabhail (Barn) (pron. SAUL) County Down, Northern Ireland.
Legend says Saint Patrick died here and received his last communion from Bishop Tassach. The first church founded by Saint Patrick is located at Mag-inis. The ground is considered holy.

Ard Macha or Armagh (Macha's Height) Northern Ireland.
Saint Patrick built the Cathedral Church and founded the See of Armagh in 444 AD. The Primate of the Church of Ireland is housed there today. Two ruins nearby on Tóchar Phádraig Saint Patrick's Road are Struel Wells and a rock formation called Saint Patrick's Chair that is part of Struel Hill. 

Croagh Patrick (Patrick's Hill) Westport, Co. Mayo.
Mountain where Saint Patrick spent 40 days of Lent praying and fasting. Hundreds of people go on pilgrimages to Croagh Patrick on the last Sunday in July. A.k.a Ireland's Holy Mountain, the Reek(3) County Roscommon Saint Patrick founded the church of Aghanagh and Shancoe in this county. At Clontusket Priory is a carving of Saint Patrick crushing the devil with Saint Catherine.

Ballymote Near County Sligo.
Saint Patrick founded the parish of Taunagh, and consecrated Bishop Bron.

Kells, Island of Stone Kells (Head Fort) Co Meath. 
Monastic remains of a round tower, stoned-roofed building, and the Patriccii et Columbae Crux (The Cross of Patrick and Columba) are here with four other stone crosses. In 807 AD Monks created The Book of Kells, which is an illuminated manuscript of the gospels of Matthew, Mark, Luke, and John at the monastery.

Inchagoill (Island of The Devout Stranger) Lough Corrib, Co. Galway.
Contains the runes of the fifth century Tempull Phádraig made of limestone and an eleventh century church called Church of the Saints. A.k.a. Island of Stone, because of a two foot high stone pillar, the Stone of Lugnaedon. The pillar was discovered in 1810. 

Donagh-Patrick (The Church of Patrick) Co. Meath.
The Church of Patrick was built here and the region named after it. (3) Trim County na Mí, Ireland. Saint Patrick consecrated the Bishop Mel here and oversaw the building of Rahan Church which is part of the Diocese of na Mí or Meath.

Dunshaughlin Co. Meath.
Domnach Sechnaill church was built and the first hymn composed in Ireland was written by St. Sechnall. It honors Saint Patrick, is 23 stanzas long, and is known as Hymn in Patrick's Praise.

Wells and Caves 

Dublin (Black Pool)

Saint Patrick's Cathedral (built on Saint Patrick's Day 1192 over four older churches) has a stone slab called Saint Patrick's Well Stone. The stone covered the remains of Saint Patrick's Well from the ninth century AD, where Saint Patrick baptized converts and was unearthed in 1901.

Bally-lig-Patrick (Patrick's Hollow) In Ballymena.
A cave and ruins of ancient buildings known as Saint Patrick's Tower are here.

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