I need a lot of help

How about this itinerary:

3/14 - 3/15 Dublin
3/15 - 3/17 Belfast
3/17 -3/19  Galway Belfast connecting in Dublin (6hrs by train)
3/19 - 3/21 Cork
3/21 - 3/22 Dublin My flight leaves at 8:30 PM

It looks like I might be in Belfast during Paddy's day. A good idea or do it the opposite way starting Galway, but it seems that I'd be back tracking . Please any input would be appreciate thank you 

Larry
You might have to rein in the itinerary as a  week not enough. I would do Dublin then Cork then Galway. It's 3 hours by bus between them. Train ok but very busy and it's limited.
Dublin Belfast Galway Dublin is another option. Day tours run from Galway to Cliffs of Moher. 
Again ask for help in tourist office. They are very good. Just mind your bags in city centre.Temple Bar  Dublin ok during day. Too many drinkers at night. 

Forgot to say taxi from airport expensive. Dublin bus will bring you to city from outside the door. Aircoach, a private bus also does a trip stopping at various hotels around the city. Can be useful. Information on their websites.

Hi Mary

Oh I thought it was double based on the information I got from Elizabeth. So you think that allowing 2 days per town is not practical. I'm aware the traveling between Belfast to Galway is almost half day trip via Dublin. That's why I removed Clare from my itinerary. I could take one day upon my return to Dublin since I'd have the entire day on 3/22

Yes. I already read about taking a taxi from the airport would be expensive.  That's why is so important to find a B n B near a bus or train station.

A must of me is Cliffs of Moher, Belfast and Cork not too much into Dublin thou. As far as the train goes I'm a bit confused there are several types of trains DART, and I forgot the other one. But you think taking the train would be too limited. I'm not too crazy about traveling by bus too confining.

Another idea = from original itinerary 
CORK TRAIN TO DUBLIN 2 HRS 39 MINUTES Stay a day or two then
 DUBLIN TRAIN TO BELFAST 2 HRS 35 MINUTES  stay a day or two
 BELFAST TRAIN TO DUBLIN CITY CENTER , Bus to airport 
I don't care for backtracking , I'd rather go in geographical order as much as possible .go to furthest point first
then work towards last stop before home , less stressful . 
Remember starting out you can take city center bus from airport to city center train station
then Train ( DUBLIN TO GALWAY   = 2 HRS 13 MIN ) 
or a bus right outside airport to Galway about 3 hours .
Elizabeth 

Dart train is only a coast line in Dublin. LUAS is a cross city tram system in Dublin. Irish rail if you really want trains. I mention the bus because they are often a far more efficient service. I think Elizabeth is right. Leave Dublin til last. Cliffs of Moher are in Clare and the only way to get there is by car or bus  day trip.  Belfast a short journey by train from city centre.Galway 2 and half hours by bus direct from airport. By train you have to get to Heuston Station first. So perhaps
Dublin to Belfast direct then to Galway and Cliffs Of Moher.  Cork  then back to Dublin. Good luck. Whatever you decide you will enjoy it. Remember to bring the raincoat.  Mary.

I rarely spend any time in Dublin. I land there then leave to go elsewhere . I have made a few exceptions for a play at the Abbey Theater or a special Dinner and Storytelling at Brazen Head pub the oldest pub in Dublin a special evening is called  Food Folklore and Fairies. 
I suggested the hop on hop off bus to give you a real feel of the city and best sights . 
While at the cliffs of moher I walked to nearby place called Gus O'Connor's Pub Traditional tavern, opened in 1832, offering Irish food, outdoor benches and nightly live music.in  Doolin, County Clare, Cash-only · Cozy · Casual Opens 9:30AM. . I always have had great food
and listened to the traditional music . In Cork you can visit Blarney Castle but the English Market is a must stop they have great offerings 
 Traders selling organic and locally produced food in an 18th-century covered market..I always take a bus from Cork City to a small little town called Clonakilty for more music in a club called Debarras's a tiny place with amazing history . I hope this helps some .
Elizabeth .

Thank you Mary and Elizabeth. Are you two related by any chance? I just noticed you both have the same last name.

You both have no idea how much I appreciate all the effort and help you both have been to me. Thank you so much

Mary
You said:

So perhaps Dublin to Belfast direct then to Galway and Cliffs Of Moher.  Cork  then back to Dublin.  Mary.
I think you are suggesting to pass Dublin completely and go straight to Belfast upon arrival. My flight gets in around 8:30 AM. So I thin the train that leaves closed to 1 PM would be better. There's one at 10 AM, but I'd hate to take any chances.
3/14- 3/16 Dublin to Belfast
3/16 - 3/18 Belfast to Galway (Via Heuston Station then take the tram to Connolly station. I believe if I purchase the ticket Belfast to Galway the tram transfer is included to go from Heuston to Connolly. Is that right?
I think with two days I could have a chance to see Cliffs of Moher

3/18 - 3/20 Galway to Cork ( bus I think)
3/20 - 3/22 Cork to Dublin. I would have almost 3 days. Do you think I should stay in Dublin only 2 days. And if so which town would be better and cheaper to stay 3 days.

I hope I am not going to keep you both bother, but trust me writing to you both its a great sounding board.  
Elizabeth, I appreciate all the suggestions you have given me to see during my visits to these town. But honestly, at the moment I'm more concern with my itinerary than sightseeing. The other issue is most of the B n B are not centrally located. I'd prefer to be near the center of town. Thanks

That looks like a good itinerary Larry.
Galway a small city. B&Bs on College Road is near the train and bus station.
In Cork, Western Road is about 15 minutes walk to City. Lots of B&Bs there. Cork is not huge either.
Belfast, I am  not as familiar with.
For reasonable stay in Dublin try Hostel World.com, they have some good suggestions for Dublin centre. Most other B&Bs are a short bus trip away. Not related to Elizabeth. Burke a common name in Ireland.
Cheers
Mary

Hi there,

It seems like Mary and Elizabeth were able to help you plan the perfect itinerary, Larry!

Regarding finding the perfect accommodation as central as possible, maybe our accommodation search tool will be of help.
You can view the results of your search on the map, to make sure you get the best location based on your itinerary.

Regarding the transport, I will advise you to have a look at our Public transport article that includes useful links as well as details on a travel App/website that can be handy while planning.
Depending on the type of transport you are choosing you may have to purchase different tickets including transfer.
This and the timetables may also impact the time you will spend on the road and potentially your itinerary.