Dublin and what other city in Ireland?

I (American/single woman) live in Cork county and far prefer Cork city to Dublin. It's very walkable and stressless. You can take the train a short trip to Cobh (pronounced Cove) from where the Titanic made its last voyage.
Long distance buses go everywhere in Ireland from Cork. The train system isn't that extensive.
If you needed to get back to Dublin look into Ryanair from Cork (and I think they still fly from Kerry).
May is the most beautiful month to visit the area IMO.

Tenaya, thank you!
Is there a particular part of Cork City that I should stay in? Can you offer any suggestions of hotels and pubs?

County Cork lov eit it is all so good. Here is a good website http://www.cork-guide.ie/

You could also look at maybe going from Dublin to Belfast
The enterprise Express train service does the journey in about 2 hours and using Belfast as abase get buses to do trips like to Giants Causeway or the Bushmills distillery

What is your budget???

Based on your interests, I would recommend going from Dublin to Belfast. When we visited our daughter there, who was studying at Queens University, we did quite a bit of walking in the city and the University area. The Botanical Gardens are lovely and for a pub, don't miss the Crown Bar Saloon. I also recommend taking the hop on/hop off sightseeing bus, especially since it will take you to Stormont (Parliament building) which has some nice gardens and walking paths.

The Bushmills Distillery is along the Antrim Coast and I imagine you can find a tour that includes it along with a stop at the Giant's Causeway which shouldn't be missed.

Should you decide to visit Belfast, take a look at the Avenue House B&B for your accommodations. It's a very nice place in a great location. If you enjoy walking, it's within walking distance of the University, the Botanical Gardens and the city center. (We walked to all of those places from Avenue House.)

I am a travel agent and specialize in Irish travel. You might want to consider doing a railtour. They have everything from day trips, overnight, and 2 - 6 night tours, using the rail system in combination with a motorcoach while in your destination. You're accommodations are included and the services of an Irish driver/guide who will provide great insight to local history, customs and folklore, adding a great deal to your travel experience. Also, if I must be honest, I think a 4 or 5 night stay in Dublin is overdoing it a little bit. Unless you really like visiting a lot of museums and doing the theatre. Otherwise, you could do a city bus tour the first day seeing the highlights and then revisit the ones that interested you most the following day. 2 nights, possibly 3 would be what I'd suggest. If you need help booking anything, I'd be more than happy to help.

Thanks for all who have replied.

Tenaya, I can't believe I omitted such an important detail! Was hoping to keep my lodging under US$125 per night, would prefer under 100.

Longhorn55, Bushmills sounds interesting, just need to figure out transportation--will look for a tour and see what my options are. If you have experience with a particular tour operator, please feel free to suggest! Not sure about Belfast--was thinking of splitting my time between Dublin and Cork, but will do some research.

Mactravel, thanks for the suggestion. I was planning on 4-5 nights in Dublin, figuring I would do at least one day trip. Also, I will be flying in from the United States on my first day, so was trying to allow for a slow first and second day. I may trim it to 4 nights and then move on to another locale in Southern Ireland (Cork or Kilkenny or ???).

Thanks to all who have responded. Please feel free to make suggestions.
Aloha
Kaneohe

Galway, love everything about Galway and there are plenty of day tours from the bus station in town. You can take a ferry to the Aran islands, see the cliffs, the Burren, Doolin, Lahinch and north to Cong and Kylemore Abby at reasonable prices. Galway had great hostels that are a good price. I have stayed at the Forester but know there is a good selection. You can take a bus to Galway or the train. Cheap.

We took a bus to Galway.. a pleasant spot ( it was too crowded in August) Aran was the one place we really liked in Ireland.(one can take a small plane).
In Dublin, take DART to some small towns on the Bay. We loved Sandy Cove.

South-West Ireland which includes the towns of Killarney, Dingle and Kenmare is the main tourist area outside Dubln. On this board Dingle has a lot of supporters but in truth the town is small and it is the local area that makes it attractive,as is the case with Killarney too.There is a train from Dublin to Killarney every 2 hours from Heuston Station and the journey time is about 3h 30mins. Book the ticket online to get best value at www.irishrail.ie

Thanks again to all the suggestions--this board is a great resource!

I fly into London on May 9 and plan to connect straight to a flight into Dublin, spending 4 or 5 nights there with at least one day trip out of Dublin. Then I will move to another location for 2-3 nights--will get started researching all of your suggestions and will get back to you all with more questions.

Thanks again for your time!

Crazychick has it about right. The Antrim coast road from Belfast is definitely the best drive in Ireland. It's beautiful. Take the bus. There's lovely fishing villages at Carnlough, Cushendall, Cushendun. All totally unspoiled. Can't beat it,