1. Bimble around the east end: if they're into culture there's the Whitechapel Gallery and Rich Mix; if they're into record shops there's Rough Trade and Sister Rays; there are a few good independent bookshops between Brick lane and Broadway Market; loads of options for tasty food on a budget (bagels, curry, generic street food in the Truman Brewery on a Sunday); go for a pint in the Carpenters Arms on Cheshire St; take them to Broadway Market on a Saturday if they like flat white's, craft beer and generic hipster shit, take them to Colombia road on a Sunday and they can buy you flowers or a house plant as a sign of their appreciation of your hospitality; take them to Freedom and the Cable St Mural if they've got good politics
2. If you have to go to the west end: spend most of your time in Soho: its got good food on a budget; the best cinema (Curzon Soho); Foyles, China Town, record shops around Berwick Street, Old Compton St. Refuse point blank to take them to see the queen/parliament/houseguards parade. Only go to Trafalgar Square for a demo, or the National Gallery at a push. You could walk through Hyde Park to the museums in South Kensington though, but refuse to take them to Harrods. If you go to Portobello Road have a coffee in the Spanish supermarket and spend more time at the Goldborne Road end than the Notting Hill Gate end.
3. if you take them to the South Bank don't go as far east as Tower Bridge or as far west as the London Eye/Westminster Bridge
4. Avoid the City of London like the plague... unless you have a good reason for going to the Barbican, or they're really into the psycho-geography of central business districts.
5. If they don't like cities take them to Epping Forest. If they like cities and the weather is good take them to the park. If they're a hipster go to London Fields. If they're a bird spotter, or have an appreciation of bleak edge spaces, take them to Rainham marshes.