I'm actually running a Star Hero campaign without any alien species right now. I've explored some of the same questions, looking at how human culture develops in absence of other intelligent alien species. The campaign basically hypothesizes that, with humanity's uniqueness in the universe being confirmed by a lack of contact with other sentient races, human culture would develop around basic principles like:
1. Embrace your humanity: with no other races showing up, humanity is increasingly celebrated as something special and unique in the universe. "Human-ness" is elevated and idealized. Technology is designed to integrate as seamlessly and invisibly as possible; cybernetics, AIs, and the like are seen as an undesirable diluting of that which makes humanity unique. However, technologies that blend with humanity more naturally (biological modifications and so on) are much mroe accepted.
2. Work hard, play harder: Humanity's undisputed dominance (and implicit arrogance) has resulted in an increased emphasis on recreation and fun. Humanity is a great thing, and you can't exactly celebrate humanity by working your entire life away. It's not total hedonism, but work and play are seen as equally important parts of life.
3. Live in the now: Since humanity is the ultimate form of life in the universe, why dwell on the many imperfections, growing pains, and stumbling blocks of its development? Being wracked with guilt over the past, or cripplingly worried about the future, doesn't do much to celebrate our essential humanity. Again, this doesn't mean total hedonism, but rather an increased appreciation for spontaneity, impulsiveness, and fun.
4. Accentuate the positive: Sure, humanity has done some stupid things, but why dwell on it? Humans are as good as it gets, and there's really nothing else to look up to, so its better to stay positive and focus on the good things in life. Droning on and on about this or that injustice begins to feel increasingly preachy to people -- after all, we're *humans.* There's no doubt we'll move past all that in time.
5. You Deserve It: Why feel guilty? Humanity may use up a lot of resources, but there's nobody else out there who needs them. Ultimately, the more unique humans are, the more they percieve a have a right to enjoy themselves regardless of the consequences. Whatever consequences human actions have are for humans to deal with, so why feel bad about it?
There's probably more, but this post is getting ridiculous.