One thing that is difficult to convey is the scale of space. "Space... is big. Really big. You just won't believe how vastly hugely mindbogglingly big it is...". I think this website does a good job at getting a sense of the size of our solar system and how small we actually are. After looking at that you can watch this and realize just how small the Sun is compared to other stars. Then remember there are around 300 billion stars in the Milky Way and there are over 170 billion galaxies in the observable universe...
What's cool though is that we can and have sent spacecraft to check out nearby planets, moons and other interesting objects. Right at this moment there is one orbiting Mercury, a few orbiting the Moon, one roving around Mars, a couple orbiting it and one that's going to land in August, one that's in the asteroid belt, one on it's way to Jupiter, one flying around Saturn and one closing in on Pluto. We have landed things on the Moon, Venus, Mars and Titan.
For better or for worse (I think for better) the space shuttle program was shut down and people seem to think that NASA must not be doing anything then! Although it's true that the overall human spaceflight capability is quite crippled right now it's encouraging to see the commercial space industry up and coming with companies like SpaceX, Blue Origin and Virgin Galactic. In fact SpaceX is testing it's space capsule (unmanned for this test) and attempting to dock at the International Space Station within the next week or two.
Although human spaceflight is much more difficult then sending robotic probes I think it is also much more inspiring. Landing a person on an asteroid or Mars is such a massive undertaking that it would likely require international cooperation and is something that I think the planet as a whole can rally around. Yes there are problems on Earth and there always will be, but I think humanity is capable of multitasking.