Here is a list of countries and places I would would recommend seeing or I would like to visit myself.
(Places in Italics are places I have been to)

The United Kingdom of Great Britain and Northern Ireland
England
• Elizabeth Tower and Westminster (More commonly know by the bell 'Big Ben' inside it)
• Tower Bridge
• Tower of London
• The British Museum
• The Shard
• Luton Hoo
• Bletchley Park (in Bletchley; not in bloody Milton Keynes!)
• Silverstone
• Oxford
• Bath
• Hadrian’s wall
• Stone Henge
• The Globe Theatre
• The Seven Sisters
• Tintagel Castle (A contender for Camelot Castle)
• The Channel Tunnel
Scotland
• Edinburgh
Wales
• Snowdon
Northern Ireland
• Giant’s Causeway

France
• The Varenne river
• Notre Dame
• Louvre
• Eiffel Tower

Monaco
• Monaco

Germany
• Freising & Weihenstephan
• Neuschwanstein Castle
• Brandenburg Gate
• Prora

Poland
• Auschwitz

Russia
• Kremlin

Spain
• Calat Alhambra
• Sagrada Família
• Parc Güell
• Las Ramblas

Gibraltar
• Rock of Gibraltar

Portugal
• Madeira

Italy
• Venice (my favourite City on Earth!)
• Uffizi
• The Duomo
• Mt. Vesuvius
• Pompeii (the scale of it city is extraordinary)
• The Herculaneum (much more well preserved then Pompeii)
• Naples (there is no traffic in Naples, just one big car park)
• Ravello & The Amalfi Coast
• Sardinia & The Emerald Coast
• The Roman Coliseum
• Leaning tower of Pisa

Vatican City
• Sistine Chapel

Greece
• Parthenon
• Delphi
• Phidias' workshop

Croatia
• Krka
• Trogir

Cyprus
• Tomb of the Kings

Turkey
• Mausoleum at Halicarnassus
• Temple of Artemis
• Hagia Sophia

Jordan
• Dead Sea
• Petra

Egypt
• The Great Library
• Lighthouse of Alexandria
• The Great Pyramids (Right in the middle of a housing estate with flying nappies and a MacDonald just around the corner)
• Mt. Sinai

Ethiopia
• Danakil Depression

United Arab Emirates
• Burj Khalifa
• Burj Al Arab
• Bur Dubai
• Wild Wadi

Morocco
• Marrakesh

Mali
• Great Mosque of Djenne

Senegal
• Lake Rebta

Tanzania
• Lake Victoria
• Mount Kilimanjaro

Madagascar
• Forest of Knives

India
• Taj Mahal
• The Red Fort

Sri Lanka
• Adam’s Peak

Tibet
• Mount Kailash

China
• Emei Mountain
• The Great Wall
• The Forbidden Palace
• The Terracotta Warriors

Hong Kong
• Avenue of Stars
• Victoria
• The Big Buddha (Do you like stairs? Great fun though!)
• Macau

Japan
• Himeji Castle
• Tokyo Tower
• Mt. Fuji

Cambodia
• Angkor Wat

Indonesia
• Borobudur Temple
• Krakatoa

Singapore
• Singapore

Australia
• Sydney Opera House
• The Great Barrier Reef
• Pink Lake
• Uluru (Ayer’s Rock)

Canada
• Big Tub Harbour
• Bay of Fundy
• CN Tower
• Niagara Falls

The United States of America
• Broadway, New York
• Statue of Liberty
• The Empire State Building
• Central Park
• Ground Zero/The Freedom tower
• Pentagon
• Old Faithful & Yellowstone National Park
• Grand Mesa
• Barringer Crater
• Miami
• Disneyland Florida & Universal Studios Orlando
• The Grand Canyon
• The Hoover Dam & Lake Mead
• Painted Desert
• Petrified Forest National Park
• Aircraft Boneyard
• San Andreas Fault
• Las Vegas (my first ever upside down roller-coaster was the one at New York New York hotel!)
• Hollywood
• Alcatraz
• The Golden Gate Bridge
• Route 66

Mexico
• Chichén Itzá
• San Juan Parangaricutiro Church

The Bahamas
• Grand Bahama
• Nassau

Venezuela
• Angel Falls

Colombia
• Caño Cristales

Ecuador
• Galápagos

Peru
• Machu Picchu
• Lake Titicaca (Underwater Ruins)

Bolivia
• Cerro Rico & Potosí
• Uyuni Salt Flat

Brazil
• The Amazon Rainforest
• Cristo Redentor
• Iguazu Falls
• Pantanal

Antartica
• Blood Falls