best places to visit after 4 days in London

Well it's hard to answer without a little more information: are you tied to flying home out of London? Can you fly home from somewhere else? Have you been to Paris? How many nights total do you have in Europe - not counting traveling days. If you really have 8 days, meaning you have 8 nights to sleep in Europe, I would do London and Paris if you've never been there.

If you want to stay in England and you have fewer days to travel, I would consider York. Easy train connection and a nice-size town with quite a few sites.

Drive to Lake District or Cotswolds or visit the Jurassic Coast. Train to Durham for a couple of days. Or York. Or Edinburgh. Fly to Dublin or Amsterdam, or Berlin, or Barcelona. Eurostar to Paris..

If you are staying in England I suggest Bath for a few days, then York. If you have a car you can go to Stonehenge on the way to Bath, and on to numerous destinations around Bath. We saw what we wanted in Bath in 3 days. My wife and I recently saw the St. Fagans Museum of Welsh Life (Outdoor) on a day-trip from Bath - we thought it well worth the drive. Another possibility is driving from Bath to the Cotswolds - we did that on a previous trip - seeing Tintern Abbey on the way and used the Cotswolds base to see Stratford upon Avon, Blenheim Castle, and Warwick Castle. I have not used the train or buses there but I imagine they would work. Or take the train to Bath and rent a car there if you want to take driving trips. I would definitely not drive all the way to York! Beginning September 1st many sites close earlier.

Chris , I think you should not miss Yorkshire / city of York. It's quaint easy to walk around see the shops , York Minster "walk to the top " , walking the Roman Wall's that are around part of the city. For 200 years this was held by the Vikings. Then driving in Yorkshire is just beautiful with pubs located in the countryside "met the locals with their dogs " , some of the old churches nearby. The people are so friendly , proud of there history and I have never found anyone who would not stop and chat with a visitor , One place to see is Rievaulx Abby in North Yorkshire , Helmsley and you can spend the night here next to the Abby . I was just checking it out last week as I would love to do this. Check out the website , looks like it would be a real treat just the opposite of London. Moors , Dales with lovely valleys you drive through. One day we even drove over to Whitby a Whaling port where river Esk flows into the North Sea . One of the best fish & chip shops in all of Yorkshire is located here! Wonderful views of the houses on the hillside at the port.. You won't be sorry if you go to Yorkshire..
Not too long a ride on the train as I have met a few people from Yorkshire , Scarborough areas who had been to London for a day of shopping. Also on one of my return trip back to London from York the train cars were full of Scot's "going to a football game in London ".. So you could do York and then visit Scotland for a couple of days. Hadrian's Wall would be neat to see " I did a online college class from England about this. The Roman's built this in between the wilderness "Scotland " and England .

The Cotswolds would be a great place. You can take the train from Paddington in London to Moreton-in-Marsh, it's a - 1/2 hr trip. There are two options, 1) rent a car from Robinson Goss (robgos.com) which is about 6.5 miles from Moreton-in-the-Marsh, which you could take a taxi to. 2) when you arrive take cab to the B&B you are staying at then use buses to get to other villages. But, the bus doesn't go to all the villages, I know that you can get a bus to Bourton-on-the-Water, Broadway, Moreton-in-Marsh, Stow-on-the-Wold, Painswick and Chipping Campden. Depending where you get on the bus you might have to change buses in Moreton-in-Marsh.
Having a car would be the best way to go.

My suggestion if I had 7 or 8 days, I would go to Bath and York. You can take a train to both places and you don't need a car. I have been to both cities and loved them both. Both are really quaint and charming cities to visit and tons of places to visit. Get the RS England book and read up on where to go and what to see. Just two small lovely cities. If you don't want to stay in England, I would take the train to Paris and spend the whole week there. You can see and do a lot in 7/8 days in Paris and still not see it all. Paris is an amazing city and easy to get to by train from London. You can't go wrong with either trip, Bath/York or Paris. Whatever you choose in England or Paris it will be wonderful. Have a great safe trip.

"are you tied to flying home out of London? Can you fly home from somewhere else? "

This is a very important point. While London, of course, has by far the most nonstop flights to the US, it's not the only city with nonstops. Edinburgh, Glasgow, Manchester, and Birmingham have some flights to JFK, Newark, Philadelphia, etc. And with one change (often in Amsterdam, Dublin, or London), you can fly to all kinds of UK airports.

Of course, if a roundtrip flight to London works best with your itinerary, fine. But, for instance, you may want to start in London, head north to York, then further north to Edinburgh. You can then fly home from Edinburgh or Glasgow, removing the need to get back to London (and using up a travel day in the process).

A great way to find out quickly who flies out of an airport is to look at that airport's Wikipedia page. Of course, you then have to confirm directly with the airline.

Thank you to everyone for the great advice. Based on your input, I'm leaning toward Bath and York. But the Cotswolds sound good too. So hard to decide, and yet for me, planning the trip is a lot of the fun. We'll be flying on miles so we're not stuck on returning from London. Paris is fantastic of course but we were actually just there last year. Hmmm, Bruges doesn't look too far...

Don't overlook taking the Eurostar to Paris, 2.5 hours, city center to city center. See www.seat61.com. Tickets go on sale 6 months prior to your travel dates and are dirt cheap but go up alarmingly as the date approaches. Get on www.tripadvisor.com, Paris forum, for detailed advice about hotels, transportation, advance tickets, restaurants, shopping, etc. You can take a day trip to Amsterdam, Brussels, or other cities near Paris.