G-dog likes shooting things and driving cars. So I would wish to combine those two passions and give him a new toy- a death star. First of all I believe that flying should be a lot cooler than simply driving a car. Another reason is that if I remember right G-dog doesn't like to be surrounded by people. So he could have a lot of personal space...in space.
I am sure that any gun collector would be happy to have Death Star in his collection. You might think that Death Star is an overkill for a weapon. And of course you would be right. But who cares that thing looks cool. You don't even need to be a star wars fan to appreciate it. It seems that building a Death Star would be quite an achievement for us. For better or for worse it could be another world wonder.
Another reason why I would give Death Star to G-dog is because I believe that he would use it reasonably. With a great power of such massive weapon many people would be tempted to become a space dictator. But I trust that Galen would not become power crazy. He seems like a reasonable person and he already has experience with weapons...even if it is not on the same scale. In fact having someone we can trust in control of the Death Star could be quite handy if it turns out that humanity is not alone in the universe. Should aliens come to earth with bad intentions Galen and his Death Star could help us save humanity.
Obviously I could never afford to build a death star. So I would use my wish to give it for G-dog.
Sorry for lack of words- I can't think of anything more to say.