Known Space... Yes yes yes!
An upvote is not enough to express my agreement with that suggestion.
Niven is the author of some of the best sci-fi ever written, IM not so HO.
It would, however, need a very good director, given the quantity of asides and introspection in some of the works - try getting the narrative from Protector, for example, into a TV/Movie friendly format without loosing the subtlety of the Pak's worldview and without turning the Pak into Hollywood Terminator-style psychos.
Some of the collaborative Kzinti Wars stories would be eminently filmable as long as the director could resist the temptation to portray the Kzin as Simba-in-a-Spacesuit, as some of the less able cover artists of the volumes on my bookshelves have regrettably done.
Oh, and I'll see your Larry Niven and raise you an Alfred Bester - The Stars My Destination would be a fun movie for those raised on sci-fi that relies more on thought than on CGI pyros.
There's a lot of written sci-fi out there, especially from the mid 20th century, that Hollywood and TV have overlooked and which could usefully be examined instead of the current vogue for weakly re-making other's works of twenty or thirty years past.
But then again, as a friend of mine was given to observing, the pictures are always better on the radio, not to mention the printed word.