I should also add: is there anything over-rated that I should skip?  I'm on the fence on the Titanic Museum, for example... 

bump!  I know there are lots of UK nectors on these boards - any one?  any one?

Lyric Theater in Belfast by O'Donnell and Toumey. They have a lot of work in Dublin as well worth checking out.  The Irish Film Center in Temple Bar and many other interesting things in Temple Bar as well, despite lots of tourists. There is a book called Temple Bar The Power of an Idea that shows many of these projects. The Berkeley Library at Trinity College if you like Brutalism, if you are nice they will let you in, but no photos inside.  It is also next door to the Old Library/Long Room which is pretty amazing as well.   Anything by bucholzmcevoy architects for nice detailing.  http://www.bmcea.com/

Stags Head, Toners, Long Hall for pubs, O'Donoghue's Bar near Grafton St has good smoked salmon. One of the best things I ate in Ireland.  Bernard Shaw has a younger crowd, woodfired pizza served from a bus in an outdoor patio. The street it is on Aungier, Camden is worth walking down to the canal.  Walk from the Liffey up O'Connell St. to the Hugh Lane Gallery. Lots of Georgian townhouses around St. Stephens Green and Merrion Square.

In Belfast, walk down Falls Rd. (catholic) cut over thru one of the gates in the wall to Shankill Rd. (protestant). Lots of political murals, ect. I was there while some of the marches were going on, so did it in the morning. Eat an Ulster Fry somewhere. I saw the Titanic Museum being built, didn't do much for me. Bittles Bar and the always crowded Crown Liquor Saloon.  Belfast also has an architecture center:  http://www.placeni.org/whats_on 

Do you know where you are staying? I'm sure I can remember some more.

Oh, this is great!!  Thanks sjniles!  I didn't know of those firms - super great help, thanks.

In Belfast we're staying at a b&b pretty centrally located (it's not a big city anyway).  Can't remember what street it's on.  We have more days in Belfast since we're visiting family.  I've seen some of the parades... fascinating and chilling at the same time.  My family grew up just off the Shankhill - I know it well.  Haven't been there in years and have always been ensconced with family so haven't had too much chance for sightseeing in Belfast yet - so I'm really looking forward to this chance!

In Dublin we're trying to stay away from Temple Bar area (for quietness' sake) - currently looking at places  around St. Stephens Green or near the Canal... haven't found the right place yet.  If you have any recommendations I'd love them.  We're running into a LOT of hotels & b&bs with bad reviews, and not many without.  It's kind of like Lagos in that respect... I think it's a hazard when you're visiting one of the "party cities" of Europe, for better or for worse.  

For b&b's have you seen http://www.number31.ie/ . It wasn't in my budget but I visited a friend who was staying there and he loved it. I actually rented an apt. thru airbnb and it was great, if you've never used it check it out.

I can understand avoiding Temple Bar but there is some stuff there worth checking out as I mentioned above. The Photographic Archive and Meetinghouse Square, and the Black Church Print Gallery are worth spending some time in Temple Bar. A couple other Irish architects in addition to the ones above to check out are McCullough Mulvin and Grafton Architects.

I really enjoyed walking around Belfast. If you get out to the Lyric, the Ulster Museum is on the way and is somewhat interesting.

I'd also say if your time is limited in Dublin maybe skip the Guinness factory. Or just go directly to the pint and view of Dublin at the top. I was there five weeks so did go eventually but if my time was limited I would skip it.

Cafe Noto has good coffee and wifi and is across the street from the National College of Art and Design, which also has a gallery.  The Bald Barista on Aungier St. has great coffee and wifi as well.

Edinburgh - you'll need to walk through a few of the terraces to understand the way Edinburgh's formal and historic architecture is reflected in the static social hierarchy in the city. 

There's not much visible contemporary architecture in the city that doesn't conform to the corporate crapifesto.

Starting at Waverley Train Station: on one side is the fruitmarket gallery, currently showing Dieter Roth's diaries. What's not to like?

If you must go to the Scottish Parliament and/or castle, now is your chance be sure and go up some of the stairs, particularly Martin Creed's work no. 1059, aka The Scotsman stairs, aka the marble urinal. 

Back through the station to The Ingleby Gallery for Scotland's most important artist: Ian Hamilton Finlay (more of him later). The Ingleby used to be housed in the home of the Inglebys on Calton Terrace. The houses there are gorgeous, but if you can't get inside...

Now you are ready for Broughton Street, and the cafés from there cut across through, say, Circus Place and Stockbridge towards either the back side of the Botanics, or towards the Dean and SNGOMA. You could also detour past the Scottish National Portrait Gallery which has been recently refurbished. The facade is ornate red sandstone.

At the Botanic Gardens (home to a nice Edward Cullinan, and some sculpture in the landscape by the likes of Andy Goldsworthy and also) home to contemporary art in a classical setting at Inverleith House.

The Dean Gallery and Scottish National Gallery of Modern Art are (better for art than their architecture, but still) glorious. There's a Charles Jencks landform, and Edward Paolozzi's recreated studio among other wonders.

If you have a car, go to Jupiter Artland (really top notch sculpture in the landscape), and/or Ian Hamilton Finlay's fecund wonder Little Sparta (needs booking).

Avoid the queues at that illuminati chapel thing by not going (or go very early in the morning).

There are a few Basil Spence projects, and of course the Adam's work is dotted around. 

If you just want to gawk at lovely terraced houses: Stockbridge.

I haven't mentioned the two joined galleries in the Princes' Street Gardens. They have some masterpieces among the collections.

"you must go for a beer on Rose Street" everyone seems to say. I can not imagine why. 

Enjoy.

Fantastic, thank you!!

sjniles - we'll be sightseeing in Temple Bar of course but I just want to avoid actually staying there.  I've heard a lot about how noisy it gets at night and the hotels around that area seem more like hostels.  Thanks for the time-saving tips - I didn't even know about the pint and view.  

Psyarch - thanks, this is hugely helpful!  We actually decided to completely skip the Castle because a) we only have a day and a half and b) it is exorbitantly expensive.  Also I keep reading people saying there aren't very many rooms open to see.

Which is the illuminati chapel you mention?   There are a handful of chapels on the Royal Mile that I had earmarked to poke my head in at... but do NOT want to get stuck in crowds.

Indeed, I studiously avoided Edinburgh castle throughout 17 years of Scottish residence. 

I was referring to Roslyn Chapel which has suffered much like Notre Dame du Haut with new coach car parks and the hordes those coaches bring. 

With just a day and a half, unless you are a dedicated sculpture park fan, you won't make it Jupiter Artland or Little Sparta which is a shame. They are two institutions with globally important work.

If avoiding crowds and sensing the city is order of the day, the walk from Broughton Street through to the Dean Gallery/SNGOMA will please you. The nicest cafe off Broughton Street is probably the Broughton Delicatessen on Barony Street. An early trip up the Scott Monument might help you get your bearings, though I've never been up to check (they have a virtual tour on their website).