Irish Rail website - http://www.irishrail.ie/home/
Bus Eireann journey planner website - http://www.buseireann.ie/inner.php?id=232
Renting a car would give you more flexibility, as trying to co-ordinate train and bus times with the amount of time you wish to explore in Cong, just might be problematic.
I wouldn't worry unduly about driving on the 'wrong side' of the road especially if you have done it before. In any event, there is motorway, all the way from Dublin airport to Galway city, which would give you plenty of time (2.5/3.0 hours driving time) to get used to the 'wrong side', and then from Galway to Cong is on typical Irish roads - take it easy, and you will have no problems.
Tis a long way to go for a pint, for the pub will likely be the only place open in Cong in February. The Quiet man Bridge is on the South side of the Lough past Oughterard which will have more life. You could of course spend the night in Ashford Castle by Cong and make it a trip out one day and back the next. Having just got onto the boat at Dublin after driving across from above Loughrea I can tell you you don't want to be driving the M6 after dark.
If you are planning a trip to Cong whilst staying in Galway (40mins away) bring some shoes for walking as Cong is best explored on foot and spending an hour or two there. The main places to see in Cong are a stroll through Cong woods by the river to Ashford Castle, its a hotel but the grounds are beautiful on the lake shore of Lough Corrib.
Visit the "Monks Fishing House" a historical stone house in the middle of the river which you can walk out on to. The Abbey is beautiful but old and its a preserved ruin, it dates from the sixth century so its not as decorative as others. The gardens and grounds are kept well and rivers are all around the Abbey.
The Pub is open which is a replica of the interior, they only used exterior shots of all the buildings all inside scenes where done in Hollywood.
If you go to the tourist office or local bookshop get a guide to the Film scenes and locations which walks you around to each house, buildings, the church or location, it takes time but you see more of Cong.
Cong is very popular with visitors both international and domestic but it has many different qualities which attract people are:
Fishing on the rivers or Lough Corrib, Salmon or Trout
Game Shooting in the Winter
Boating/Sailing/Cruising on the Lake
2 x art galleries
History of the Abbey and surrounding historical sights like the Stone Circle etc
Ashford Castle, either to stay, eat at or just walk around and enjoy the views
Extensive mapped and Loop walks, Mountain bike trails through the woods and lake shore.
Indoor Equestrian Centre
Irelands School of Falcrony, Hawk walks
Golf at Ashford Castle
All of the above attract lots people to Cong its not just the film, which attracts its fair share too and those people are most welcome too.
Most visitors are on a 20 min to 30 min bus tour stop, and the above attractions can not be experienced in a short time.
Craft Shops, Galleries and Cafes re-open around Valentines weekend and places to eat are The Hungry Monk Cafe, best for coffee. Lydons Lodge and pub, Ryans bar for evening food.
The Lady's Buttery Craft and Art Gallery stock all handmade crafts, woolens, Bog Oak Sculptures and paintings which are always interesting to view.
The Guinness family chose to live in Cong and Ashford was there home, King George V of England stayed here fishing and shooting, Oscar Wilde lived here in his family summer house. The sixth century Monks chose Cong to build and Abbey, John Wayne drank lots in Cong, Ronald Reagan stayed in Cong as President of the U.S and scores of celebrities and Hollywood stars
have stayed in Cong so I am sure it has some special to offer, but give it time to explore and enjoy
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If you are staying in Galway and only want a day trip to Cong I would recommend going with High King Tours www.highkingtours.ie. It seems to be the only dedicated tour company from Galway to Cong. It is a fully guided tour taking in Ashford Castle, Cong Abbey and Cong Village. It is run by a local person with a passion for Cong