We are flying into London, and back home from Dublin. 14 days to see England, Scotland and Ireland. I know it's not a long amount of time, but we like to move around. Suggestions on towns and things to see, where to stay and how to get there is appreciated!
Fourteen days might be enough for Scotland. It won't touch either Ireland or England. Look at the transit times - - it doesn't work. Since you've apparently already bought your tickets, make it England and Ireland, but you won't see much of either. Maybe London and somewhere close, then Dublin and somewhere close.
You really don't have time to cove that much territory. I recommend a week in London with several day trips (lots of possibilities- see website at end of this post). Then spend 1 or 2 days in Dublin , then move to somewhere on the Dingle pennsulia- you'll need to rent a car in Ireland. Do day trips from there. You'll save money if you rent a house or aparement in Ireland and an apartment in London. http://www.aaacarolinas.com/Magazine/2008/Jan-Feb/britain.htm?zip=28105&stateprov=nc&city=matthews
Will you br driving? Taking the train? Your mode of transport will make a difference. And - wow. There is so much to choose from, it would help the commenters to know your personal preferences. Are you museum lovers? Are you outdoorsy? Are you foodies? History buffs? Royal watchers? Beer drinkers? Do you hanker to see the Big Famous Sights, or do you prefer off-the-beaten-path sorts of things? Do you care about standing stones and menhirs and Merlin, or could you happily visit the UK without stopping off at Stonehenge? Do you love great cathedrals? Are you music lovers? What period of music? Do you like the Beatles? Do you watch "Coronation Street?" Have you ever dreamed of taking a picnic and hiring a punt? Do you watch soccer? Cricket? Darts? How about stately homes? There are oodles of places like Chatsworth to visit if you like glorious old piles where rich folks lived. And cemetaries! I think you could almost focus a tour on seeing weathered old headstones in romantic countryside.... So - yes, lots and lots to choose from. If I were you I would start by thinking about those questions, and then I would rent a couple of travel DVDs to see what tickles your fancy... or you can buy DVDs on this site. Oh - and what about Wales? I am utterly in love with Wales... there's plenty to see there, too - right on the way to Ireland.
I'm a little more optimistic than Ed but you can easily spend 14 days on either island. I suggest you get Rick's books on Great Britain and Ireland. Pay attention to his recommended priorities. Decide how you want to split your time between the islands. For GB Rick would have you go to London for 3 days. Bath for 2 and Edinburgh for 2. York would get 1 day. In Ireland Dublin would get 2 days and Dingle 2. I think he then has Belfast but I think that's with a heavy dose of political correctness. IMHO, I think you should give more weight to GB. I'll throw out a suggestion for you to consider and others to refute. After arriving in London, start in Bath for 2 nights. Go back into London for 3 nights. Take the train to York and stay 2 nights. Go onto Edinburgh for 2 nights. Hop over to Shannon and visit Dingle for 2 nights (You'll need a car here). Drive to Dublin through Cashell (see the Rock of Cashell) and Glendalough. You'll probably need to spend the night in Cashell. Finish up in Dublin but consider seeing Newgrange/Knowth if you can. Personally, I'd pick one island and see more of it.
Four days in London with one day-trip to a place of your choice: Bath, Cambridge, Cotswalds, etc. Four days Edinburgh with one or two daytrips. Fly to Dublin, take the train to Galway, drive a rental car all over western Ireland. Return to Dublin to fly home. Get books for all the options for things to do in these countries. In London, if it's your first time, Westminster Abbey, Buckingham Palace, Trafalgar Square area, are basic sights. RS has walking tours for London. Many museums are free: the British Museum, National Gallery, Tate, Victoria and Albert, etc.