Space exploration's values divide into two categories: human curiosity, and free enterprise (capitalism).
The first category holds scientific inquiry -- how does the universe work? What are the chemical and physical properties of other objects (planets, moons, asteroids, etc.)? Is there life elsewhere? etc.
The free enterprise motive is in some ways stronger, because an immediate profit is a strong enticement. Can chemicals be harvested (and the absence of this possibility is what slowed down the exploration of our moon, since the first astronauts did not find any evidence there)? Will persons pay to travel in space (as a thrill or unique experience)? Can any engineering or manufacturing processes benefit from being carried on in space (an example might be the manufacture of ball bearings)?
The "cons" of space exploration, besides the inherent risk of traveling in a rocket, etc., are the differences between "dreams" and reality -- a "romantic" imagination can take over a sound business mentality. Some "investors" in space exploration are actually only seeking historical fame. Of course we may not like what we find in space -- a dangerous alien "virus" or a superior life force, or a discovery that negates whole trains of mathematical and physical "truths," forcing mankind to abandon large ideas.
And, of course, there are questions of religion vs. science. For example, my grandmother was disappointed at the moon walks, saying "we always thought the angels lived there."