hmmm... let's see... Big Ben Houses of Parliament. London Eye London Aquarium (built underground) Westminster Abbey St Pauls Cathedral National Gallery (free) National Portrait Gallery (free) British Museum (free) Museum of Natural History (free) Victoria & Albert Museum (free) Imperial War Museum London Dungeons Tate Gallery Thames Riverboats Tower Bridge Madame Tussauds Tower of London (where the Crown Jewels and the Beefeaters are) Carnaby Street Chinatown Royal Festival Hall Buckingham Palace how long have you got...
I live in the UK in the midlands so I would suggest you get out and about and visit some of the countryside that we have around here. Town wise, you would visit Stratford-on-Avon to see Shakespeares birth place.
New England is beautiful in the fall especially. The Appalachian mountains in the western and northern parts of New England are great. I like the rolling hills in Vermont, the White Mnts. in New Hampshire, and Maine has a rocky coast that's second to none. In southern New England, the coastline isn't nearly as rocky as Maine's coast is. Which coastline is more pretty, the rocky shores of Maine or the continuous coast of Rhode Island and Connecticut, is a matter of opinion. I like them equally as well, although there aren't any decent-sized beaches north of Portland, Maine. Maine's beaches, such as Old Orchard Beach, are in southern Maine. The diversity of New England is something I've always enjoyed. And most would agree with me that New England is a great place to vacation.