Just booze tasting or stuff in general?
You could visit a brewery, there's at least 3 in London (Young's, Fuller's and Meantime) but unless you're interested in the process then you're probably better off just going to a pub. Pubs I'd recommend:
The Cittie of Yorke and the Princess Louise in Holborn, actually come to think of it it's easiest to look here
http://www.beerintheevening.com/pubs/mostviewed/. Sam Smith's pubs are generally pretty good and pretty cheap and I'd avoid Wetherspoons.
For cocktails most of the higher end bars can be a bit expensive, especially the ones at hotels. Places to try are The Experimental Cocktail Club in Chinatown and Lounge Bohemia in Shoreditch though they are a bit full of themselves and service isn't that friendly.
You can get decent offers at restaurants at toptable.com, and if there's any specific sort of place you're looking for I can probably point you in the right direction.
For shopping, beyond the usual Oxford St, Bond St, Savile Row, Jermyn St you could visit Lambs Conduit Street a bit further West. There's some nice shops and pubs and its a bit quieter. Marylebone's quite nice as well.
If it's your sort of thing there's also the English National Opera's production of The Damnation of Faust directed by Terry Gilliam opening on 6 May, or there's The Hurly Burly Show at the Garrick Theatre which is coming to the end of it's run.
You could go to a football match, but I'm not sure how easy it'll be to get tickets for any of the Premier League teams, assuming there are any matches while you're over. You could try one of the lower league teams but I'd avoid Millwall if you can as their fans still have a bit of a reputation. There might be rugby matches on as well.
Also, while it might seem more convenient to get the tube everywhere it is sometimes nice to get the bus as you get more of an idea where things are. If you are going to use the tube, remember these things:
- walk down the left of the escalators, stand on the right and don't just stop when you get to the end
- know which lines you're going to use and in which directions.
- if at all possible, don't use the tube during rush hour