The best of England within two weeks?

I second the suggesstion of the London School of Economics. There are also some YHA Hostles in London and other rentals or budget accomodations to consider. If I had 2 weeks in the UK I'd do something like this London 5+ days (might base there the whole time...) see Tower of London, Westminster, British Museum, markets, Kew Gardens, possibly other sites do day trips by train to any/all of the following: Windsor (a must), Canterburry, Stratford-upon-Avon, Bath, Winchester, Dover, Brighton, Cardiff, York etc. Then (if I didn't stay in London and do more day trips), I'd train to any/all of the following: York- 1-2 days Edinburgh- 1-2 days Aviemore- 2-4 days (possible day trips to whisky distilleries & Blair Castle, tour local microwbrewery, canoeing, horseback riding, restored steam train, hiking, Mt. Caringorm hike or use funicular...) Inverness- 3-5 days (possible day trip to Orkneys, day trip to Isle of Skye & Eliean Donan Castle, cruise up Lock Ness see Urquart Castle, crusie on firth, etc.)
Glasgow- 1-2 days

"Mist" see sites are many but without knowing what your interests are, difficult to say which you and your friend might enjoy. As you love doing the research buy the RS Guidebook and read about all there is to see in England and the remainder of the UK. Who knows you might want to see both Stonehenge and New Grange which are a sea apart. If London is included in your plan be prepared for it's cost. Not the cheapest city on the planet to visit. An extraordinary city for sure but not inexpensive. Start looking RIGHT now to see if you'll be able to get rooms in June at the London School of Economics. Riding buses in England might be cheaper than traveling by train but those costs won't be easy to calculate until you figure out where you want to go.

Toni has some excellent suggestions. I'd add that, if you post your basic likes and dislikes, folks here would be better able to help. I would also suggest that you drop into a nice pub first thing at every town you hit, strike up a conversation with someone who looks fun and see where that takes you. I've had some of my most amazing travel experiences by hooking up with locals. Highlights have included a home-cooked dinner and a lesson in making black current liqueur, attending a local cricket team's match, going to heavy metal festival on a small town square, and attending a harvest festival with an absolutely amazing collection of antique pre-gasoline tractors.

Personally, I think Toni is overly Scotland oriented (not intending to start an argument) especially since your post stated England but Claudia nails it when she says you need to determine what the "must see" sites are for yourself. Everyone here has an opinion and I'm pretty sure none of us would only send you to the "perfect" sites for you. Two weeks is tough especially with your comment about "wanting to be temporary locals." You can't fit in and take advantage of local activities if you are only there one or two nights. Also, realize that when you go from one point to another you will spend anywhere from four to eight hours being a "local" on a train or in a car. You could certainly spend a great trip in England (or Great Britain) with places with good rail and bus connections. These types of trips require good planning unless you're willing to redo your trip plans frequently during the trip. Also, the amount of traveling you do will have a significant impact on your costs. Any idiot can put together a trip plan with a car. At this point I must state, I mostly use cars to get around. Unfortunately, cars require parking which is all usually expensive near most hostels.

Josh, Riding the rails is fine, but you're at the mercy of their schedules. The upside is being able to travel from place to place at night...sometimes. Mind you, I like riding train but if you have only 2 weeks, try to get talked into hiring a car. Must sees of course differ from person to person. York, Stonehenge, London, Oxford or Cambridge (I'm usually in the minority in suggesting Oxford) and not in this order. If there is time the seaside is always fun. First choice, Blackpool, but its a long way out of the way. Second choice Brighton. Driving, watching people have fun and English TV should be "must do's" for every visitor. Ditto Kira's post.