Buses can be pretty awful – I should know, I have to use them every other day or so! They’re always running late or cancelled with no warning… At least with trains you have the departures boards so you know what’s happening and when. Bus timetables are almost never right.
You should definitely spend some time in London, because it’s the biggest and most interesting place in the UK by a mile. As for other places, Oxford and Cambridge are kind of the same as each other but both pretty spectacular and a lot less noisy/crowded than London. Lots of amazing old buildings. The Lake District is one of the more scenic areas in England. There are even more dramatic landscapes in Scotland, Ireland and Wales but they’re not as easy to get to.
In terms of travel, bus is quite cheap but takes ages and is unreliable and difficult to use. Trains are easy and quick but very expensive unless you book in advance, so it depends how good your finances are. In London, book a hotel near a tube station (try http://www.tubehotels.com) and travel around on the underground.
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