Modern or classic? Big or small? There are so many amazing hotels in London - I contract London hotels for a UK tour operator, these are some of my favourites:
Me London is on Aldwych, near to Covent Garden, very modern black/white decor, the Radio bar on the roof is great for a pre-theatre cocktail if you can get in
Across the road is One Aldwych, fantastic restaurant Eneko on site, bedrooms are quite simple for a 5* hotel and no coffee maker, but service is great
If you want something more classic, my favourite is the Langham, bedrooms were refurbished last year, it's very close to Oxford Street.
Near Green Park is Sheraton Grand The Park Lane - it had a full refurbishment last year and is now modern in an art deco style, it's really lovely but not as iconic as Langham or Ritz for example.
Another great 5* is Rosewood, near Holborn. The building is old, but the rooms are modern but still cosy, not contemporary like at ME.
If you want something lovely but not quite at these budgets, look at Amba Charing Cross or Radisson Edwardian Mercer Street - rooms have complimentary soft drinks and the higher category rooms get more "extras" so although they're not 5* hotels, they feel more special than your average hotel.
Not quite as central but still easy to get to everything is The Ampersand in South Kensington. So easy for Harrods, V&A Museum, Kensington Palace. A bit more boutique than the others I've mentioned.
Things to do ... London Eye is still incredibly popular, and the champagne experience was really nice, but for views, the Shard has it!
Afternoon tea has to be done! I haven't done lots, but my favourite so far was Emmeline's lounge at Conrad St James - no views from the lounge, but the food was amazing.