Verdict first: Day 1 landmarks + West End show, Day 2 history, Day 3 green spaces + Harry Potter; 3–4 days covers the highlights, 5–7 for a deeper visit. Day 1: Palace of Westminster & Big Ben, Westminster Abbey, London Eye, Buckingham Palace (Changing of the Guard Mon/Wed/Fri/Sun at 10:45am), then a West End musical. Day 2: Tower of London (900 years, Crown Jewels), Tower Bridge, the Shard's 72nd-floor deck, St Paul's Cathedral, and the free British Museum (Rosetta Stone). Day 3: Warner Bros. Harry Potter Studio Tour, Hyde Park (350 acres), Kensington Palace, King's Cross Platform 9¾. Use an Oyster card or contactless card for the Tube; the London Pass saves money if you visit many sights.