If ever you are at a loss as to where to eat, have a coffee, meet a friend, or just while away the hours over a good book in the heart of London, then I really recommend that you visit this wonderfully charming cafe in Marylebone: Paul Rothe and Son. There aren't really so many cafes like this any more, where there should almost be a charge that you pay in order to be able to have the privilege of paying again for the pleasure of sitting there and eating or drinking! There has been a cafe / shop here for over a century and the reason for its longevity is surely the good nature of the family that have run it since it started.
To be at at loss + as to + where / when / who / why / what + infinitive:
'I was at a loss as to where to go after work'; 'I was at a loss as to who to speak to about my problem'; 'I was at a loss as to how much to pay the waiter'.
To while away the hours
'To pass time in a leisurely way' - generally when we while away the hours or time, it's doing those pleasurable things that may not seem to be too productive to the rest of the world (like reading a book with a cup of tea or coffee and a delicious, sweet, naughty snack)!
This is a noun that is used to describe the state or condition of lasting a long time: Rolling Stones are known for their longevity (as are turtles - the animal, not the band!).
'.....the reason for its longevity is surely the good nature of the family that have run it since it started.'
The reason for X is Y: the reason for + noun phrase + is + noun phrase:
The reason for my cold is the cold weather.
The reason for my lateness / being late is the inefficiency of the London Underground.*
*this is is just an example; the London Underground is one of the most efficient underground railway systems in the whole of London (or even the 'hole' of London).