I will be in New York on business and am querying transport - do I need to get a car or is public transport good. Places I have to get to are:

Harris Road Bedford Hills
East 40th Street New York
Prospect Street Beacon

At the moment I am still trying to find some accommodation so I am not sure where we will be exactly but perhaps given these locations, someone can also advise on accommodation - 3/4 star hotel perhaps?

Thanks

So will you will be in Manhattan most of the time and just need a trip to Beacon and Bedford Hills? All in one day? Several trips to each location? A car makes sense only if you need to be in several locations on one day. New York area traffic can be very busy, even in the "opposite direction" (leaving Manhattan in the morning and returning in the evening)
East 40th street is very close to Grand Central Terminal which is where you would get Metro North trains to Beacon and/or Bedford Hills. Once you arrive, you will need a taxi or someone to pick you up from the nearest train stations to get to your specific addresses.

Beacon and Bedford Hills are more than an hour north of NYC by the trains described, but are not that far from one another. If you rent a car and your schedule allowed, it would be easy to visit both locations in one day. Or you might choose to rent a car to visit the two, then use the train for you visit to Manhattan.

Without knowing the schedule of how all these stops relate to one another, it's difficult to give the best advice.

As others have said, you can use Metro North trains from Grand Central terminal to get from Manhattan to both Bedford Hills and Beacon, (look at Harlem line here http://www.mta.info/mnr/html/mnrmap.htm) but once you're there, it depends on whether you have multiple sales calls to make in those areas or are just going to one place in each. If you decide to stay in/near Beacon or Bedford Hills, you'd need a car to get around. If you decide to stay in NYC, a car will be a liability as parking is expensive and driving in the city is discouraged.

and am querying transport

Depite great support, it is still illegal in NY.

It is 45 to an hour by car from Bedford Hills to Beacon because there is no direct route.

Beacon is on the Hudson line of MetroNorth.