Like most big cities, the more populated areas are fairly safe. Foxtown/Greektown/Joe/RenCen square area isn't too bad, and there's a lot of places in the suburbs that are worse. Though I wouldn't want to hang around Hart Plaza or Campus Martius at night (though there isn't any reason to anyway).
Eastern Market, Cass Corridor, the bridge area, Belle Ilse, any of the projects...those are places to avoid. Fortunately, there's no reason to go there at night unless you're looking for trouble.
The real problem with Detroit is that other than the casinos, there's nothing there that you can't find better, safer, and more convenient in terms of parking/cabs in the suburbs. I love SE Michigan, and hate the bad rap the city gets, but compared to say Royal Oak, Ann Arbor, or even most of western Wayne county, it does kind of suck.
The douchebag quotient is way less in downtown Detroit than Royal Oak or Ann Arbor!!!
I kid, I kid, I'm a Royal Oaker and I love it here.
I've never gone to Harpo's as I've never had a reason to, but I've heard nothing good about its surroundings.
The neighborhood that Harpo's is in sucks, its basically the type of neighborhood that Detroit gets its bad reputation from. However, if you want to see a metal concert, no other venue compares