So much to see...
Obviously this is very very very subjective and there is too much too see - so here are a few inspirations from my wife and my experiences. Your tastes may vary.
2 of us "did" England, Scotland, Wales, Eire and a splash or Northern Ireland in 2 weeks. Run the whole time. See much. Collapse exhausted when you get home.
FWIW our look-around philosophy is like yours and less like some respondents'. Given 2 weeks in a large area we would rather run like mad and see a little of as much as possible, rather than have an in depth look at some small part. We would love to see more detail everywhere, but you can see so much in one day in an area if you are prepared to push yourselves to the limit. This is not everyone's idea of how to holiday !!! :-).
Get a National Trust pass. Expensive - and worth every GBP of it. Cost based on duration. Buy shortest snd sell/give to friends. Then have free entry to so so so much. Castles, gardens, more. Not everything alas.
If want beautiful/amazing/weird/impressive/utterly different - see Portmerion. Utterly fake and artificial - but also marvellously mystical and 'romantic'.
A longish haul to the coast but things to see along the way and utterly astounding. The ITV program "The Prisoner" filmed here. All my life I'd longed to see it, never expecting to. I was so pleased to be able to do so. Alas, a vast number of other people want to do so too. That's life. Avoid weekends I guess. Great. DO NOT get caught by the tide - dangerous bore. It's mainly "The Prisoner" fans who do that.
Photos composite below is from above site:
Portmeirion - Wikipedia
Portmeirion images and links - worth a look
If you like technology at all, even just driving past Jodrell Bank will excite you. Talker to far flung Space Craft, searcher for aliens, listener to stars. Very impressive.
There are two working boat lifts in the UK - taking barages / canal boats and flinging them (not overly fast) skywards or down.
One is a wheel - The Falkirk Wheel.
And the Anderton Boat Lift old and restored and marvellous in quite different ways.
Also : http://canalrivertrust.org.uk/Anderton-boat-lift
Oxford is worth a quick peek.
All the colleges - often open to public view.
All closed the day we passed through :-( - except one.
Which was the one I most wanted to see ! :-) - Magdalene - C S Lewis, Old building, history, impressiveness, choir stalls carved to exquisite perfection, more.
See a few Cathedrals.
Plenty in Europe but the British ones are also good.
Super special for us - may or may not be for you:
Coventry Cathedral !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The symbol to the Bristish people in WW2 of stubborn and resolute resistance.
The bombed shell defiant against the foe.
So, after the war, did they rebuild it, did they raze it ?
Yes and no. Inspired. The outer wall of the old rebuilt somewhat, clkear open space in middle. Plaques. Performances, ... ,
And next door joined at the hip the new "modern" Coventry Cathedral.
Ground glass angels like you've never seen before, or since.
The then largest tapestry in the world (French made) at the front.
little alcoves and chapels and nooks. A feeling of real understanding of the message of Christ. Of Peace & love & reconciliation and servanthood and ... .
If that is not you it may not be you. For me it was stunning.
And, of course, the church is twinned with a sister church in a German city.
Lest we forget !
All images below from Wikipedia.
Walk where Churchill walked 70 years ago.
See, almost, what Churchill saw, plus, now, so much more.
You can fly into eg Dublin with minimal loss of time. Rough and ready and cheap sometimes Ryan air will have you there in under an hour as I recall and off the plane so fast you'll wonder what happened. We stayed in a hostel on Batchelors Walk about 30 seconds from the very centre of Dublin. Marvellous. A few days in Eire allows you to see much.
If you want to see a real castle then Raglan Castle in Wales is superb. The last to hold out in the Roundheads/Cavaliers war. 14 foot thick stone walls in places (really). Much remains. Moat amazing. Separate keep accessible from main castle with its own moat.
If you want to see a picture book / calendar / chocolate box castle (you do!) see Bodiam Castle, somewhat south of London. If you see a castle on a chocolate box there is a good chance this is it. It looks right, feels right, set in a pretty mote/lake, across water approach pathy, turrets , walls, all the right stuff.
Its "real" and it also "fake". Its a real castle BUT it was buolt as much for show as for defence. Walls are far thinner than Raglan. 30 bedroorms - a 30 room party house. Guests from all over, entertaining, social status etc. STILL worth seeing. Very very pretty. Nice feel. Good photos.
Many Bodiam Castle images here - DO look
Just a few views:
If you spent your youth reading Wordsworth and longing to see Tintern Abbey you can - at last. But they shut it after hours.But just the drive down the Wye valley, thickly thatched cottages, little pubs, utter English country beauty is magical.
Images below from this wikipedia images search