Dublin in May for family of 5, with or without breakfast?

I enjoyed my stay at Zanzibar Locke, which is an apart-hotel (24-hour front desk staff like a hotel but rooms with kitchens like an apartment). My room would easily have accommodated your three daughters, as it had two twin beds and a couch that appeared to be convertible (or at least not the worst place to sleep). Locke has another location out towards the docklands area that has 2-BR suites. I found the price very reasonable. Zanzibar was located by Bachelor's Walk on the north side of the Liffey, and there were loads of shops (even a shopping mall), bars and restaurants nearby, so we were able to get some groceries. There was also a coffee shop in the lobby.

We've stayed at 3 places in Dublin over the years, and we like all three:
Harding House (don't get the breakfast, there's a great coffee shop a couple of doors down). Across from Christ Church.
O'Neill's Victorian Town House near Trinity College (small kitchen available, no breakfast, but excellent options nearby)
Skylon Hotel near Croke Park (good options both with the hotel and nearby cafes)

These are not luxury accommodations but very clean, comfortable, friendly, and great locations.

I have friends who live in the Ballsbridge area just outside the City Center. It's a semi-residential area with guest houses and hotels. I haven't stayed in any of them (we stayed with our friends). The area is clean, safe (many of the embassies are located there) with plenty of cafes and restaurants and access to public transit. It's also walkable to the St. Stephen's Green area of the City Center. The only place I know that serves afternoon tea is the Merrion Hotel, a five star property with a price list to match.

Thank you all for the very good information. As I checked all of the hotels mentioned I found that many had deals for booking in January, often 10-30% off. My preference is to book a cancellable reservation so right now I'm trying to decide between Harding Hotel and Trinity City Hotel, both without breakfast included. Trinity is about $400 more, which is significant but is considered a 4 star hotel (not sure that means too much to me.)
What about the 2 areas? Harding Hotel is next to Christ Church Cathedral, a little more central, but Trinity city Hotel is closer to Book of Kells, Trinity College and EPIC museum. Since we'll be in Dublin for 2.5 days we plan to hit many of the sites, which are all across the city. I'd love to hear any opinions on the areas.

We are just back from Christmas in Dublin. It is quite walkable in December so May should be lovely. We stayed in the Davenport , though not planned. We booked The Mont and were informed it would be closed for a short time for renovations. The Davenport , Mont and a few other hotels near by are part of the O'Callaghan Collection. The hotel I understand was an upgrade but they honored our booking price. It was very nice, huge rooms, nice staff and we had a breakfast included rate. The Davenport is central near the parks , close to Trinity College. I wandered over to see Christ Church Cathedral, beautiful architecture , though I did not like that area as much as Merrion Square and St Stephens Green. I had originally looked at the Trinity Townhouse Dublin in my hotel search. We walked by it on our visit and it looked really nice, street location and all. Enjoy your stay , may will be a beautiful month.

Sheila, thank you for your post. Glad to hear that you found Dublin very walkable in December, that bodes well for us in May. I did check out the Davenport and the Mont, both look lovely although a bit more expensive than our current options. I'm curious about your thoughts on the different neighborhoods. The Trinity City Hotel is closer to where you stayed, and it seems like that is a nice area. We are also looking at 2 places closer to Christchurch cathedral, which seems slightly more central. Did you go to the Guiness Storehouse? If so did you walk it, or use bus/tram?