QPR

You can get there either by the Hammersmith & City line, or by Victoria and Central lines. The Hammersmith & City option to Shepherds Bush Market is better for a pre-match pint. Either way you'll need a One Day Travelcard (zones 1 & 2). Coming back it's White City and the Central line, changing at Oxford Circus to the Victoria line.

Pubs
There's absolutely nothing in the immediate vicinity of the ground - the Springbok, on South Africa Road, is home fans only nowadays, and the big pub on Bloemfontein Road (General Smuts or whatever its latest name is) is very dangerous and is to be avoided. There are though plenty of options vaguely en route from Shepherds Bush station to the ground - see the pub map below. A lot of them will no doubt be very busy, but those in question haven't got much going for them anyway! My recommendation is the White Horse on Uxbridge Road. Most people won't even notice it, and if they do they'll probably walk straight past because it looks tiny and nondescript. However, once inside it's like the tardis, and it's friendly and cheap, and it has a beer garden. And on top of all that it's run by a Geordie couple! If the White Horse does happen to be too busy then I suggest you try the Crown & Sceptre or the Greyhound. If you'd rather be a bit closer to the ground then your best bet is the British Queen; there are a couple of places very slightly closer than it, but you'll never get served in them.

For more info on getting there, pubs, etc check out:
Internet Ground Guide
London Transport
Pub map
Kings Cross pub map
Pub guide (by Burnley London supporters - very comprehensive!)