I do not think we will ever run out of things to know in space. Even if we gain a complete understanding of the universe, which does not seem likely to happen any time soon, there are still an infinite amount of places to travel. The edges of tthe universe are infinite so by definition, it is not possible to reach the edge and know everything there is to know.
There are big questions to answer in space but there are also small questions to answer. For example, we will never know the geological make up of every planet and every star.