I'm an ancient old fogey so I won't attempt to suggest lively places for a 21st birthday but I'll have a go at suggesting some hotels:
Just how rich is your boyfriend? London is the dearest city in the world for hotel accommodation, so 5-star hotels won't be cheap! As an example of accommodation prices in London, I know a pub, near Waterloo station, which charges �80 per person per night. That's just for pub accommodation, so you can guess what some hotels charge!
So, having pointed out that a pub charges �80pppn, I was amazed when I checked on the prices at the Langham Hotel. I expected that they'd be at least �300 pppn but, on the random date which I've just checked, I've found that, for a twin-bedded (or double-bedded) room, their price is just �120 per person. (For comparison, the Savoy, which is no 'posher' than Langhams want at least �200 per person, with prices rising to over �300 per person).
The reason I checked the Langham's prices is that the hotel offers the height of luxury. The Langham is the oldest of London's major hotels and has probably had more royalty and state presidents stay there than any other hotel in the world. If you want to rub shoulders with the the rich it would seem to be the place to stay.
To save your boyfriend some money, you might want to consider the Grosvenor House Hotel, on Park Lane. I've heard quite good things about it and, for the date I checked, it's offering an amazingly cheap price of �75 per person.
In fact, every hotel here
http://www.viewlondon.co.uk/hotel_5_stars.html
should offer an enjoyable stay.
For even better economy (in a plush modern hotel), knock a star off and consider Jurys Clifton Ford Hotel. The date I checked had accommodation at an amazingly low price of �49.50 per person:
00:04 Fri 18th Aug 2006