Day trip from London to Leeds/Hastings/Bodiam/Canterbury

I've done Canterbury and Dover in one long day and another day did Hastings, Eastbourne and walked out to Beachy Head. You need to study the train maps as several of the places you want to see are in different directions. http://www.nationalrail.co.uk/static/documents/content/London_South_East.pdf

Pretty slim.

If you told us what interests you in each, maybe we could help sort it out.

You've plotted all four on a map, right?

Leeds is definitely the outlier, way up north in Yorkshire. And other than visiting a solicitor's office there when I bought a house it has held no attraction for me at all.

What attracts you to Leeds? The Royal Armouries have a big and excellent display there if that floats your boat.

You don't mean Leeds Castle in Kent, do you?

It is always best to be specific in the UK and follow the local custom to not abbreviate. We have a lot of places with similar or the same name and to avoid going the wrong way say what you mean.

EDIT: Canterbury (not London - finger fumble) is easy from London by high speed train from St Pancras International. If you take a traditional train from Charing Cross it will take much longer.

Hastings is also available by train from London, but on a completely different part of the rail network. It can be connected by changing in Ashford, once an hour and takes a little over an hour.

Bodium Castle - National Trust - is a one where you need to be creative. Quoted from their website:
Seasonal steam railway from Tenterden town to Bodiam station: 1/4 mile. Mainline railway stations at Robertsbridge, 5 miles; Battle, 10 miles (London Charing Cross to Hastings route) No public transport links from mainline railway stations, only private taxis. No taxi rank at Robertsbridge - need to pre-book taxis. Taxi rank at Battle.

If you do make that more complicated trip to Bodium castle, then go via Battle, where they say the taxi rank is, and so you can also include the Battle of Hastings Abbey and Battlefield (separate from the town of Hastings, on the coast).

Thanks for all the responses. I think I've got a better picture of how to work this out.
Toni