The Merchant - great location, service, atmosphere. My favorite in the city.
Culloden Estate and Spa (Virtuoso*****) - outside the city
Fitzwilliam (3 star) - good location, inexpensive
The Merrion (Virtuoso*****) - My favorite! The best!!!
Fitzwilliam - balconies over St Stephens Green, a block from Grafton
The Dylan - very chic, love the terrace bar, good restaurant, service and staff are top notch
The Cliff Town House (3 star, delightful), great location
Four Seasons - next to RDS. Extraordinary hotel if the location suits you - Be sure to book so you get Preferred Partner benefits. (FSPP*****)
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Re Belfast, if you want a convenient location and a good price you could try the Days Hotel on Hope Street. It's just a few minutes walk from the Great Victoria St bus and rail station where the airport buses drop you.
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The Westin - SPG, near Trinity College
The Shelbourne Renaissance - Marriott, on St. Stephen's Green
Conrad - HHonors, kinda average and overpriced
For a well-priced 4*property, large rooms, new build - 15 mins form city centre, in a pleasant enough part of the city, beside Kilmainham Gaol, I'm also happy to recommend the Hilton Kilmainham. I use it for mattress runs occasionally.
For 3* properties look at Jurys Inns.
Eagles may soar, but weasels don't get sucked in to jet engines...