There's loads to do in London, I wouldn't even know where to start...
but i guess I could try,
The first thing I always reccomend is the galleries, the Tate Modern in particular for its innovative handling of modern art, then if you're interested in British art and its history the national and portrait galleries are great often have fantastic exhibitions and house some great collections which are both within walking distance.
Covent garden is a great place to be during the day its got a real kitchy market feel and theres lots of street performers out and about, not to mention a great place to shop for clothes.
Check out Brick lane for a great curry and China town in the centre for a good atmosphere and really cheap fab chinese food,
Then there's always all the other touristy stuff like the london dungeons, wax works museum, the London Palladium, the London eye, catching a ferry down the thames...blah blah, all great fun to do! but watch the prices and the queues!!!
A helpful thing to do in London is to buy a time out which has great listings for shows, exhibitions and good places to eat! and although I haven't looked at it for a while I thnk it lists entertainment like music events too!..oooh do you like Jazz?? I can reccomend a couple of cool places....
My major advice is don't bother with Edinburgh this time around, the train takes a eight hours and I bet you'll regret spending what is already a short time on our grotty old English trains! (I have plenty of national pride but come on!!!)
drop me a line if you wanna know more...?
take care and have a great trip
As mim say, don't bother with Edingburugh as it is too far away to count as a 'daytrip', if you want to see somethine else apart form London while in England I'd suggest Cambridge, which is just 2 hrs away with bus, very picturesque (spell?) and different from London, lots of historical buildings (colleges)
It's a nice small town to just stroll around. You could also do the walk thorugh the meadows to this famous Apple Orchard outside Cambridge (about 45 mins walk) can't remember what it's called but you should be able to find info through the tourist information. Virginia Wolf et al have all been drinking tea in this beautiful garden..
While in London I recommend South Bank, it's such a beautiful walk and there are several (art) museums, The London Eye - where you will get a great view over London, close to many of the land marks such a s Big Ben + houses of parliament and relatively close to st Pauls cathedral, tower bridge etc.
I also think you should visit one or two of the big parks, Regent's Park is my favourite in central London, very beautiful and with a nice cafe in the middle.
If you can try to do all the travelling by bus as you get to see much more than if you use the tube.
The best way to travel between London-Paris is by eurostar. Very comfortable and it's only 2,5 hrs between central London (Waterloo) and central Paris Gare du Nord!
We recently went to Paris with eurostar for a day and had a great time.
Were really impressed with Notre Dame. Sacre Coeur in Montmartre was also very beautiful. We walked a lot and stopped at quite a few cafes for coffee and hot chocolate and also had a huge yummy lunch with some wine - which really made our day
Try not to squeze in to many things to see (it will just be exhausting and not very enjoyable in the end) but focus on a few things, take in the atmosphere and have a great time!