And yes, of course you can be 'good without God'. I suppose from a philosophical point of view Christians tend to believe that all successful goodness is a remote reflection of God's. But where motive is concerned, where adherence to a view of the world is concerned, there's obviously no necessary connection at all between belief in God and virtue. The place is stuffed with atheists and agnostics doing devotedly benign things, acting on ideals of compassion and dignity and mutual aid, relieving suffering, working to save or improve the planet. There are a lot of paths to virtue, mercifully, and absolutely no way there could be a religious or Christian monopoly on it.
The point of Christianity is not that it produces virtue. It does, I suppose, have one advantage when it comes to doing good, in that your advance certainty, as a Christian, that you're going to fail at goodness provides a kind of assurance that goodness is worth trying independently of results.
It helps a little, therefore, with being good in circumstances where doing good can do no good as far as making progress is concerned. Where things just won't get better, in measurable terms, for all the devotion you pour in. Virtuous and idealistic atheists are at work all over the place, but it is observable that surprisingly large number of believers are to be found among those who volunteer to work with the dying, the demented, the addicted, the institutionalised and the very impaired and afflicted, where the best that can be done is to love for the sake of it, and to keep sorrow company.
Francis Spufford, Unapologetic: Why, despite everything, Christianity can still make surprising emotional sense, 213-214.