Getting to the ground
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. The cheapest way of doing it though is with an Oyster Card or contactless credit/debit card. It will cost you twice as much if you pay cash, which is a ridiculous amount considering that it's only a couple of miles. A one day Travelcard is even more expensive. 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. Most of the other pubs anywhere near the ground, don't allow away fans in, or at least not if you're wearing colours. However, the Twelve Pins and the Blackstock, both close to Finsbury Park station, tend to get a mix of home and away fans. Likewise the Depot, which is a stone's throw from Caledonian Road tube. If you're getting the train down down you might prefer to sup around Kings Cross and then catch a late tube up to the ground. If so then the curiously popular Dolphin is an obvious option. You can do a lot better though, and quite a few of them are marked on the Kings Cross pub map.
For more info on getting there, pubs, etc check out:
Emirates pub map
Kings Cross pub map
Football Ground Guide
Official Arsenal site