Covent Garden to the river
The walk from Covent Garden to the river takes about fifteen minutes if you go straight down to the Embankment and do not turn into the market. In the evening the Piazza is full of people who are not going anywhere in particular, which makes it a poor place to meet and a fine place to leave. A hotel on the Strand is on this walk. A flat in a mansion block south of the river is not: that is a cab, and the bridge you mean should be named, because Waterloo and Blackfriars feel close on a map and are not close in a car at ten.
The other two notes are Mayfair after eight and a night that starts in Soho.