Windsor Castle is justly famous as a huge Norman Castle and the home of British monarchy for close to a thousand years now. If you are staying in London, then Windsor is just one hour by train. You have two routes to choose from depending on where in London you are staying.
If you are south of the River Thames, or around the strand/embankment area then go to Waterloo station and get a direct train to Windsor and Eton Riverside Station.
Alternatively, if you are in Soho or Camden, go to Paddington Mainline Station and take the train to Slough. You can change to the Windsor Branch Line which is on platform 1.
Either way, you will end up in the delightful little town of Windsor which has great restaurants, great shopping, a huge park, riverside walks, boat rides and of course, the Castle itself.
You can see the Changing of the Guard for free every other day as they march through town with full band accompaniment.
The town crier is often around at weekends delivering proclamations from a spot near the statue of Queen Victoria .
The one non-budget aspect to Windsor is the castle entrance fee which is high, but definitely worth it as you can happily spend 3 or four hours within the walls.