I think Heaven is, quite simply, the dwelling place of God. I believe the passages referring to a New Earth and New Jerusalem are literal. Humans are physical beings, why would we exist in a solely spiritual universe?
I think the afterlife for Christians, Heaven, will be life in a universe uncorrupted with sin, including sin in us. God will dwell on Earth, and we will worship Him.
I think we'll still do plenty of the things we do here: Eat, drink, play sports if we want to, (Civ 4!

) fellowship with friends, read books, etc. I doubt that we'll just stand in place and sing hymn's for all eternity, although it's possible. There will be no sin there, but many things we do are fun and not sinful; why couldn't we enjoy them there?
As for animals, there will be animals on the New Earth. I don't know if they'll be the same, as in we'll have our old pets back though.
I think of Hell less as a place of actual fire and lava and whatnot, and more as a place of eternal loneliness and despair. After all, without God, what would sinful humans make of any world? Hell. That's basically what Hell is, absence from God's presence.