a few suggestions for England only.
For cities:
London (Westminster Abbey, Big Ben, Buckingham Palace, The Houses of Parliament, Various museums and much more besides)
Bath (Roman baths, The Royal Crescent etc)
Manchester (Industrial revolution)
Chester (Roman remains)
Oxford (dreaming spires, university buildings, history)
Portsmouth (Maritime history)
Bristol (Maritime history)
Smaller cities:
Chichester
Truro
Lancaster
Salisbury
Worcester
Rural Landscapes:
The Cotswolds
The South Downs
The Yorkshire Dales
Simply stunning:
The Lake District
The Peak District
Teesdale
Wilder places:
Dartmoor
Exmoor
Parts of Northumberland
Upper Teesdale
Superb Coastline:
The Southwest Coastpath especially
Studland to Weymouth,
The western side of the Lizard Peninsula in Cornwall,
Land’s End Peninsula in Cornwall
and the North Coast, Cornwall,
Northumberland (also for castles)
London
York
Canterbuy
Chester
Peak District
Northumberland
Orkney
North Norfolk coast
Southwold
London
Bath www.visitbath.co.uk
York and the North York Moors National Park and Whitby www.yorkshire.com
Edinburgh/the Highlands/The Cairngorns/Isle of Skye www.visitscotland.com
Ludlow and the South Shropshire Hills www/ludlow.org.uk
www.visitsouthshropshire.co.uk
We have a dense frequent national rail system. You will see a lot as you travel. For best value buy a Britrail Pass before arrival
www.britrail.com
www.nationalrail.co.uk (timetable information)
Go to bruce grove at night or barking is nice also check out hackney at night . Just kidding avoid them.
Depends on what sort of things the individual likes and doesn't like
Falkirk Wheel in Scotland - you will love it!