For the West End its probably best to stay in the Victoria, Covent Garden or Park Lane areas but anywhere central is good really as you can easily get a bus/ the underground/ walk - I know for example that there are cheaper hotels around Euston, Kings Cross and St Pancras stations and also in Kensington both of which are a short journey to the area where the theatres are.Airport-wise theres not much in it - Stansted, Luton, Heathrow, City and Gatwick all have good tranport links to central London. It might however be easier to get a train because it will take you directly to the centre of London

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