9 days in Dublin. Where to visit 1 day? ie London, Stoneheng, Scotland??

One day? Why bother but if you're determined to go, you need somewhere that won't be a big problem to get to the sites from the airport. That makes London a problem since you'd spend almost as much for the rides to and from the airport as your plan tickets. I suggest Edinburgh. The roundtrip bus ticket is a little over 6 GBP. You could see the castle and a number of other sites and still make it back for your evening flight.

One day, but it comes out to about 8-10 hours. I really want to give my adult (19 and 20) children a reference so that it is familiar when they go back and spend more time without me. Also, London/8 hours/75€-roundtrip is a cheap-ish day trip, I think. I have been to London - but it was 20 years ago and all I remember is the bridge, B Palace, Beefeaters restaurant and Peeticoat lane.
I will google Edinburgh now, thank you!

I wouldn't do a 1 day visit and agree the main London airports would be impossible. But further alternatives could be to try Bristol airport which is 10 miles from Bath - although I dont know how you get there from the airport (?hire a car for the day). There is also London City Airport, but I think any flights to this airport would be expensive - closest to the financial centre on the east side of London. But you can get the Docklands Light Railway from the airport direct to the Tower of London. One advantage of London City is that its a small airport that you can get through quickly.

Katy, you would not advise flying into Heathrow?

From Heathrow you have a choice. Either the tube, which is cheap, but takes an hour to the center (see tfl.gov.uk), or main line rail, which is expensive but faster (see national.rail.co.uk).

Several years ago we flew from Dublin to Leeds airport and then went to York. We stayed overnight and continued to other sites in England, but I think you could do York as a day trip, assuming the flight times work out. Leeds is a smaller airport - once we landed, we were heading to our rental car ten minutes later.

Can take a while to get out of Heathrow, immigration lines etc. Last time I was there took an hour - was very chaotic. As Kathy says quickest is Heathrow Express, 4 trains an hour takes 15 minutes - you arrive at Paddington, and then go to ?. And on the way back you have the lines at the security checks at Heathrow to go through. There are small airports in UK that are much quicker to get in and out of.

I would still need to go through immigration lines from Dublin to Heathrow? For some reason I thought I didn't.
I just took a trip to the states and the security and imm. lines were tedious.

I don't think you have to go through passport control if you're coming form Ireland, but you will have to clear security when you fly back.

Heathrow you would have to go rgrough security when you fly out. Dublin is in a foreign country, I cant see why you would not have to go through immigration (not an Irish citizen so i am guessingn here). When you get to immigration you could be anyone from anywhere until they see your documents if you really want to use the one day to expose your children to a possible future experience, sounds like it should be London. Everybody who speaks and reads English has been exposed to its names and major sights in their reading, history etc. tube would be convenient as you dont have luggage and can end up right in the heart of all the sights Still suggest you re-thinkk the idea though. If you Really want to do it, make it two days (one night)

@Brian - a quick google results in: "CTA2.1 Common Travel Area Paragraph 15 of the Immigration Rules states that the United Kingdom, the Channel Islands, the Isle of Man and the Republic of Ireland collectively form a common travel area. A person who has been examined for the purpose of immigration control at the point at which he entered the area does not normally require leave to enter any other part of it. However certain persons subject to the Immigration (Control of Entry through the Republic of Ireland) Order 1972 (as amended) who enter the United Kingdom through the Republic of Ireland do require leave to enter. This includes: those who merely passed through the Republic of Ireland;
persons requiring visas;" and some special cases. If you look at the Heathrow website you will see that passengers on flights from Irish and UK airports arrive on a different floor to international passengers.

Kathy thanks for clarifying that re travel between Eire and UK