The Hotel Splendide that James Bond checks into in fact the five-star Grand Hotel Pupp (pronounced 'poop', I kid you not!) in Karlovy Vary, Czech Republic.
The exterior shots of Miami Airport were shot in England, here at Dunsfold Park Aerodrome
The Venetian Piazza scenes were filmed on a set at Pinewood Studios in the Albert R. Broccoli 007 Stage - famous for it's James Bond sets. The soundstage burned down during the production of Casino Royale (2006) on 30th July 2006 but has since been re-built.
The shot of Craig swiftly moving down the stairs in the 'Venice' hotel while on the phone to the Swiss banker. This is towards the end of the film.