The Public Record Office now National Archives is situated in a delightful site on the banks of the Thames and set in its own water garden.
Having researched in the PRO (now National Archives) for over a decade I can confirm that the service is exemplary - a joy to research.
I suggest that before visit that you look at the website as this will allow you to prepare the ground work for your search.
Whilst Kew is easily reach by the Tube network, this isn't the most comfortable way to travel, nor is it the most reliable. I would recommend that if you intend to visit over several days that you stay locally.
Despite the above I use the Tube arriving early, for breakfast in the Pagoda cafe, at Kew gardens tube station - a good start for the day ahead.
The water garden which surrounds the PRO provides in good weather a place to eat you sandwiches and watch the activities of the ducks and a heron.