Deep breath and ready to take cover
General thought is that the '4 miles' from CRGS can result in very different travelling times depending on direction.
Agree that West Bergholt primary has a long standing good reputation and there is reasonable bus service in to town and access to North Station.
Prettygate/Shrub End could be a good area within Colchester as its reasonably easy to get down to the A12 or out to Marks Tey station and some good primary schools. Gets more pricey as you move towards Lexden road.
To the West of town is Copford - did at one time have good primary school but dont know any thing about it now. Easy bus into CRGS and access to station. Slight issue is that the school is out of the village at the opposite end to the main road to Colchester so you could struggle to be an easy walk from both the school and the bus stop and the station!
Personally I would avoid Lexden (as opposed to Lexden Road).
There are villages of Fordham, Aldham etc but very poor bus service to Colchester.
Another option is Wivenhoe - close to University - decent schools and bus service but is the other side of town to CRGS and driving in is a nightmare. Decent train service . To drive to London, it takes a while to get to the A12
The catchement secondary for Wivenhoe has been up and down so at risk of being shouted down, it might not be a great future option as its difficult to predict how it will be by the time you might want it.
Stanway school is the catchment secondary for west of Colchester. Its reputation seemed to improve but I also know of friends who have moved their children away from there.
For the West side of the Town centre you would want to be in the catchment for Philip Morant. It has had a long term better reputation - possibly partly because it has a more middle class catchment area - although I dont have any recent experience of it.
I am sure you will get lots of help here - these are personal thoughts that might help, am not intending to pass judgement on any particular schools and hopefully haven't offended anyone.