10-12 day trip thru Great Britain

You want to see all of England, Scotland and Ireland in 10-12 days?

You're going to need to narrow down your plans a bit. Do you want cities over scenery? Do you want to have 1-3 bases or a series of one night's?

Have you looked at a map to get an idea not just of distances but how long it will take to get to each of your destinations?

Great Britain is defined as England, Scotland and Wales. The United Kingdom (UK) consists of Great Britain plus Northern Ireland. Dublin is in Ireland and is not a part of either. Are the countries you would like to visit Ireland, England Scotland?
If so, I would fly into Dublin or London and out the other. This is known as an open jaw or multi-city when booking air fare.
In Ireland I would focus on Dublin (two days and two nights) and rent a car to drive to Dingle and the peninsula (two nights) before dropping off your rental car at the Shannon airport and fly to Edinburgh on a non-stop flight that operates on certain days. After three nights in Edinburgh, you can take a direct train to York (2h 30m) and spend two nights before going to London Heathrow (3h) that'll require a connection.

Are the counties you would like to visit Ireland, England Scotland?

That's not completely clear - the UK or Ireland are countries like Canada or Switzerland are countries.

The term county as used above is like a county in the United States, larger usually than a town or a council, smaller than a nation. The four home nations of Northern Ireland, Scotland, Wales and England make up (most of) the United Kingdom.

There are currently 48 Ceremonial Counties, just in England, but these change from time to time. It is unusual for folks to be searching by counties.

Agreed that 4 home nations and Ireland is a whole big pie for just 10 days.

Can you be a bit more specific please, emtycrystal44?

I realize now that I should of said United Kingdom instead of just Great Britain. I can promise make our trip 14-15 days long instead of 10-12. I fully understand that we can’t see even a 1/3 of this giant area but I would like to see as much as possible and not just the normal tourist sites.
We have taken 3 trips to Italy and still just scratched the surface of exploring it completely,so I’m not naive enough to think I can cover all of these countries in two weeks.

10-12 days, I say don't try to do Ireland and GB. In fact, consider sticking with England or Scotland on your short trip.

We have been to England, Wales, Scotland and Ireland, more times than we can remember and there is much to see.

We did a four week drive tour (not visiting London) just for England and S. Wales in 2017.

Minimize your travel during your stay, the more time you wasted on such travel, the less you see.
London is wonderful, but you can skip it since the British countryside is amazing.
Just in England, these are our favorite places:
Bath, the Cotswolds, Salisbury, Stonehenge, Oxford, Blenheim Palace, Warwick, York, Durham, The Lake District, Yorkshire Moors, Canterbury, Cambridge, Winchester and more.
For Scotland, Edinburgh deserves 2-3 days, the area just north of Edinburgh is great, as are the Scottish Highlands, Inverness, Loch Ness and more.

I recommend reading geovagriffith's trip report as it will give you a very good idea of what can be achieved in a particular timeframe.

10 - 12 days is no time at all and even increasing it to 14 - 15 still leaves you with a limited time to fit in all the countries you've listed. You've also not given any indication of your interests so it is extremely difficult to provide suggestions particularly as you've expressed a desire not to see the usual sights.

Such a brief period will only really benefit from a visit to a handful of cities if you aim to have any semblance of a meaningful trip. I would agree with the suggestion of Dublin, Edinburgh, York and flying out of London. You'll experience a taste of very different cities with plenty to see and do (many will be popular tourist sites but they're popular for a good reason). To go off the beaten track and delve a bit deeper into Great Britain and Ireland you need significantly more time than you've got.

Honestly, if Dublin was all I had time to see in Ireland, I would skip it and spend more time elsewhere. Wales is an easy trip from London.

Are the countries you would like to visit Ireland, England Scotland?

I meant to say countries.

Not the usual touristy stuff? Fewer Americans on this forum head to Wales than to Scotland, but it has much to offer.

If you had 2 weeks, you could fly into Manchester then head to north Wales and Liverpool/Chester for the first week, which would give a good mix of cities, museums, history, castles (Conwy, Caernarfon, Harlech, Chirk etc) and Snowdonia for hills, lakes and boat rides. Take a ride on a steam train on the Ffestiniog & Welsh Highland Railways. Visit Portmerion, the Italianate village where The Prisoner was filmed in the 60s. There are numerous good National Trust properties in the area including Chirk Castle, Erddig House and Bodnant Gardens.

Second week - head to York for a few days to see the city, the North York Moors and Whitby on the coast for Captain Cook, Dracula and great fish and chips. Visit Durham and spend a day at Beamish Museum. Take a walk in Northumberland on some of the most amazing beaches in the U.K. with castles as a backdrop. I did this last week! Have a day on the magical Holy Island, if the tides permit (access by a tidal causeway). Take a day trip to Edinburgh by train. Visit Hadrian’s Wall. Take a boat trip out to see the seals.

If you don’t want the usual tourist stuff, avoid the Cotswolds, Lake District, Scottish Highlands and London.

Here is my detailed trip report
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139