I think that the overly domineering, aggressive, pushy man is to women, in some ways, what the scantily clad easy woman is to men. It might look attractive and fun at first, but you know in your head it's no good and if you're stupid enough to mess with it you know it's going to be short-lived and you're going to get burned. Badly. If you use your brain, you know that is something to run the other way from.
Being nice does not in anyway imply that you have to be fake or shallow, or that you have no spine. I am privileged to know a few genuinely good, nice, kind men who have perfectly good spines and know when it's time to stand up for themselves and others. That's the kind of man I want.
As to a man who is nice but is a spineless pushover... I try to avoid them. How can someone have your back when he doesn't have one of his own? Those men who can't deal with problems and situations gently but firmly become filled with silent resentment and bitterness that builds up over time and results in passive-aggression (which you will find rings quite true if you will read some of the resentment-filled posts on this site from this particular brand of "nice guys"...).
Then there is the superficially and selectively nice guy... like what Melita was talking about. The white knight. I dislike facades and shallowness. That's why it's good to take a look at how they treat their friends and family members. In 5 years, that's how they will be treating you, and if you get a chance to observe them around their family often, they can't keep the facade up all the time... it slips out and is a big red flag.