We'll be in London from 10/19 through the 29th, leaving on the 30th. We'd like to visit Hadrian's wall, is it better to drive or take a train? Where should we visit the wall? Is this an overnight trip? any information would be greatly appreciated.
Hadrian's Wall is 300 miles from London. By car, that's around 5 hours each way. By train, you can get to Newcastle in around 3 hours, but then you still have to get from there to the wall itself.
This website looks like it has good information about visiting by various modes of transport: http://hadrianswallcountry.co.uk/travel
While you're in London, pop into the British Museum to see the Vindolanda tablets. They're really brilliant and help make life on the wall come alive.
I'd definitely recommend an overnight near the wall. Hexham is a nice convenient town with a fine old church. There are also pubs with lodgings in some of the smaller towns close to the wall.
Train to Newcastle looks like the fastest easiest way to get there, followed by the AD 122 bus if it's running that late in the season. Or you could rent a car in Newcastle if you want to deal with left-side driving. The website posted above is full of good information.
The north of England has many sightseeing opportunities and might be worth a separate trip in the future. With only ten days in London, you might reconsider giving up two of them to see a wall -- however scenic and historic -- 300 miles away.
train to Carlisle, hire car, visit Wall
return car in Newcastle, fly home on a connecting flight from Newcastle
I paid a visit to Hadrian's Wall two years ago when I took the kids to visit my wife who was working in Newcastle during the week. We flew to Newcastle from Southampton and picked up a hire car. The drive to the wall from Newcastle took about an hour. There is a good exhibition centre there and the remains of the wall can be easily explored however although it was May the driving rain was horizontal and combined with biting winds, in late October I would expect it to be even more unpleasant.
Although I love history and the wall is interesting I really wouldn't consider travelling all the way from London just to see it, even more so when considering you're in the country for a relatively short period.
What is the main reason for wanting to visit the wall? If it's Roman history you're interested in then there's a wealth of Roman ruins and excavations to see that are much closer than Hadrian's Wall.