I am coming from Edinburgh to Stewart Airport on 14th September arriving 20.00pm, is there public transport to the city centre at that time of night?

could anyone let me know the best way to get to cheshire connecticut

Yes

Coach USA's Stewart Airport Express offer a regular service taking aprox 90 mins. Check their website for full timetable

If you mean New York City, one option is to take an Uber ride to Beacon train station and then take the Metro North Hudson line straight to Grand Central Station. You can get specifics by entering your destination in Google Maps and then selecting the route filter that looks like a train.

Yes .. buses are timed to incoming international flights