I have a method with an Object o parameter.
In this method, I exactly know there is a String in \"o\" which is not null. There is no need t
I wouldn't be too concerned by the performance, if this operation is done even just a few thousand times a second - there's no tangible difference.
I would, however, be concerned of "knowing" the input. You have a method that accepts an Object and you should treat it as such, i.e. you shouldn't know anything about the parameter, other than it adheres to the Object interface, which happens to have a toString() method. In this case, I would strongly suggest using that method instead of just assuming anything.
OTOH, if the input is always either String or null, just change the method to accept Strings, and check explicitly for nulls (which you should do anyways whenever dealing with non-primitives...)