Getting to the ground
From Kings Cross it's either:
- Hammersmith & City line to Shepherd's Bush Market (8 services an hour, journey time 20-23 minutes), or
- Victoria line to Oxford Circus, then Central line (services every 2-5 mins, journey time 20-22 minutes) to Shepherd's Bush
Shepherd's Bush Market is closer to the ground and to most of the pubs. Coming back head to either White City for the Central line, or to Shepherd's Bush Market.

There's absolutely nothing for away fans in the immediate vicinity of the ground; the Springbok, on South Africa Road, is home fans only nowadays, as are many of the pubs in Shepherds Bush. You might get in the Central (Wetherspoons), which is upstairs in the West 12 shopping centre. You'll almost certainly get in Belushi's, but you probably won't want to. It sells alcohol, but it's not what you'd call a pub, and the reviews are at best "mixed". One place worth trying is the White Horse. 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, plus the landlord's a Geordie. It doesn't have hand-pulled beer though! An alternative, and certainly better for beer, is the Crown & Sceptre, which is a bit out the way and so is quieter until very late on. It's a Fullers pub, so it's not cheap, and it does Thai food, plus burgers and chips on match days. There's also the Greyhound. All the places mentioned, plus a couple of others, are shown on the pub map below.
You could alternatively just drink around Kings Cross and then travel over at the last minute. You'd have to leave the pub by around an hour before kick-off to make it into the ground in time. Another option would be to head for Notting Hill (Victoria line to Oxford Circus, then Central line) where there are a few good pubs near the station - see the pub map below. It would then only be 5 minutes or so on the Central line to White City, from where it's a 15 minute walk to the ground. This approach would set you back another 1.50 or so with Oyster/contactless; without either of these you should get a One Day Travelcard.

For more info on getting there, pubs, etc check out:
Pub map
Notting Hill pub map
Kings Cross pub map
Ground guide
London Transport