A fabulous, inexpensive lunch spot atop tombstones in the crypt of St. Martin-in-the-Fields church on Trafalgar Square
Do not buy point-to-point tickets. What you want is an Oyster Card (possibly with a Travelcard transit pass).
Until the early 19th century, London did not have any hotels, only coaching inns, which looked remarkably like modern multi-story motels, the rooms opening off outdoor corridors. The last (partially) surviving coaching inn is The George Inn, though only its pub component is still active.