Conclusion: pick London for world icons, theatre and big-city buzz; pick Edinburgh for medieval charm and a friendlier budget. - London: Big Ben, Buckingham Palace, Tower Bridge, the British Museum; West End theatre; the Tube accepts contactless/Apple Pay — but hotels are pricey and dinner runs about £20–30 per person. - Edinburgh: the Harry Potter inspiration (Victoria Street, the Elephant House), Edinburgh Castle and the Royal Mile; walkable with many free sights, and noticeably cheaper accommodation. - The train between them takes 4.5–5 hours; allow 3–4 days in London plus 2–3 in Edinburgh. - For one city only, London is the classic pick; Potterheads and budget travellers lean Edinburgh.