I support the idea of manned missions to Mars and the Moon. Moreover I support the establishment of permanent bases because by doing so we gain knowledge of how to get people into space and onto other planets on a long term basis. Which will lead to knowledge of how to create self sustaining colonies away from Earth. Which will eventually lead to civilian colonies in said places. Which gets humanity spread out in such a away that a global catastrophe in any one place won't wipe out our whole species.
While this is happening we hopefully get a resurgence of the general population's interest in science, such as what happened during the Mercury and Apollo missions. Hopefully that interest will be accompanied by a desire for better understanding, especially among young people who will be the ones to grow up and make much of this possible. In short, such missions would be inspirational.
I know that there are problems right here on Earth that could use the space program's money and effort to great effect. But if we wait until all the world's problems are solved before turning to space, we will never get there. Although space programs are expensive, they don't take a very large piece of the national budget (less than 1%) and do not require that we abandon our other programs to fund them. We can help people right here on Earth and still go to space, we don't have to choose all of one vs. the other.