Rochester Girls is pretty good, and I think there is a good boys grammar as well. Would find out who their main feeder primaries are, if you have dc under 11. The alternative is to go further south and into Maidstone where there are 2 boys and 2 girls grammars.
Rochester has some nice parts, especially the cathedral, but it does rather merge into Chatham is where the word "chav" originated and unless you are keen on maritime history, is rather unattractive imo.
As with all areas in the country, Rochester has its good and bad areas. There a.re plenty of good grammar schools - the girls' grammar school, Rochester Maths School (boys' grammar) and the private Kings school. Chatham isn't that bad - if you avoid Luton and Weedswood areas. There are grammar schools there too - Fort Pitt Grammar school had an outstanding OFSTED report, and there is Chatham Grammar school for girls and boys, plus Rainham Mark Grammar school in Rainham (not that far away). Chatham is being regenerated at the moment and so is currently a bit of a mess, but it will get better!! It is cheap in terms of house costs and very convenient for all other areas in the SE. London is only 45 mins away by train, and Bluewater for decent shopping about half an hour drive away. M2 links very close and cheaper council tax compared to most of the country too
Be aware that Rochester itself is under Medway council - which is a seperate entity to Kent. There are lots of differences between them re schooling/transport. eg different 11+ exams and Kent subsidise secondary school transport with a freedom pass (costs £50 per year and child can catch any bus in Kent - not just at school times) but it will not cover Medway buses and you can't have it if you live in Medway. (Although I guesss that could change by the time you need them!) Also, my postal address includes the word Rochester and I have a Medway post code, but I actually live in Kent and DS goes to a Kent school!
There are a couple of montessori schhols one of which is in Strood.
Non grammars are ok, but a bit mixed so you will need to do your research. Chatham South is ok, but may be closing!!! I would avoid Medway Community College, but I hear it has a new head, so may be improving. The grammars do make for a two tier ed system tho'