Aversley Wood is basically up the A14 onto the A1, then turn off at the first exit and it's over on your left. There's a little car park on the edge of the village recreation ground and you walk up a path between that and the allotments into the wood.
It's primarily an oak and elm wood and in the spring there's a mass of bluebells on the ground. We've been a few times and one time Paul devised a walk which went beyond it which he subsequently documented via Google Maps, including photos. You can find that here.
It's well worth a visit even if you only do the wood itself. It's a wood managed by the Woodland Trust and is what they describe as "ancient semi-natural woodland" and you can find their description of it here.