It is a crying shame that Hunstanton lost it's rail connection back in the 1960's. It was before my day, but I'm still disgusted. Regular trains used to run direct from London, and would bring in holidaymakers in their thousands.
With a pathetic road connection (it's a bit better nowadays), the life-blood of the town was strangled.
The nearest railhead is now King's Lynn (direct and reasonably fast trains from London), from which a reliable coach service operates out past the old 'Royal' station that served Sandringham houses, and onto Hunstanton.
There is nothing left of the station site nowadays. It is just home a crummy weekend market.
Hunstanton stands at one end of the 'Coasthopper' service that provides public transport along the North Norfolk coast as far as Cromer. It is an area of outstanding natural beauty, and even if you have a car, it is an ideal way to explore the region.
I always think that you get a better 'feel' of a region by using such services, and this one forms a vital public service role. Whilst many around here would not dream of travelling in anything but their Chelsea tractors, not everyone around here has a choice of cars to travel in - go out and meet some real people !