Best area to stay in Manhattan and is Harlem a safe area?

It depends on where in Harlem. It is also not the most convenient place to stay to see most of the sights. Any where mid- town especially Times Square area is best . Many reasonable hotels in area. Try Hotwire secret deals and go with a four star hotel in mid-town.

What's you're definition of safe? I love Harlem and Washington Heights, but you have to have some street smarts and be prepared for the possibility of a sketchy situation, like anywhere else I suppose. Also, if you stay that far north there's a good chance that most of the things you want to see/do will involve a long-ish ride on the famous A Train. Personally, I love the A Train, but it's one of the more colorful trains in NY. If you're not interested in a little adventure I might look elsewhere.  

Harlem is fine, but personally I'd stay closer to the northern edge of Central Park than further uptown. The atmosphere's better, there are lots of good places to eat and it just felt more comfortable. My favourite area of Manhattan though, is the East Village.