The ground is easy to get to from Kings Cross - the nearest tube station is Arsenal, which is only three stops on the Piccadilly line. You'll need a One Day Travelcard. This makes it a very expensive journey considering that it's only a couple of miles, but it costs even more if you buy single tube tickets though. The cheapest way of doing it though is with an Oyster Card or registered contactless card. If you haven't already got one then you can get an Oyster Card on-line on the London Transport site (see below) or at any tube station. Getting back into Arsenal station after the game can be really bad, and you'll probably be better off continuing walking to Finsbury Park station. Alternatively, particularly considering where the away section is, head for Highbury & Islington on the Victoria line. Note that Holloway Road tube station doesn't open on match days. A further option is to walk to Caledonian Road and jump on one of the frequent buses. Or you could even just keep on walking down Caledonian Road all the way back to Kings Cross! This would take you around 30 minutes once you've got clear of the congestion around the ground. There are very comprehensive instructions on getting to/from the Emirates on the official Arsenal web site (see below).

The traditional away pub, the Drayton Park, just happens to be the nearest pub to the ground! However, as you'd expect it gets very busy, and it's nothing special in the first place. You might therefore want to consider the alternatives. If down on the train then you could have a few pints around Kings Cross and then catch a late tube up to the ground. If so then the curiously popular Dolphin is an obvious option. There are though plenty of better options - check out the Kings Cross pub map below. If you prefer to drink somewhere basically in the vicinity of the ground then my recommendations are:
- Hen and Chickens (Victoria line to Highbury and Islington)
- The George; off Holloway Road, and reasonably close to the ground
- Bank of Friendship or Kings Head, both of which are not far from the old ground
All the above get good write-ups as pubs (as opposed to match day pubs), and all are marked on the Emirates pub map below. The same map also shows a few more pub options around the ground.

For more info on getting there, pubs, etc check out:
Football Ground Guide
Emirates pub map
Kings Cross pub map
Official Arsenal site
London Transport