The ground is only a 10 minute walk from the station. If you're driving down then you'll find that the area around the ground is residents parking only. I'm sure that you'll be able to find somewhere reasonably close though.

The nearest pub to the ground is the Livingstone Arms. It's ok for away fans, but it gets mixed (at best) reviews. And it doesn't have hand-pulled beer! I suggest you head instead for the Will Adams. It's not exactly handy for the ground (allow 15-20 minutes), but by all accounts it's far and away the best pub in Gillingham. Incredibly Gillingham is the only place in the country without a Wetherspoons outlet. The nearest one is in Rochester, a couple of miles from the ground.

For more info on getting there, pubs, etc check out:
Football Ground Guide
Pub map
London Transport