all have been mentioned but;
- The girl who leapt through time
- Tokyo godfathers
- Spirited away
- Ghost in the shell 1 and 2 (movies)
- Akira (though this kind of just perpetuates the anime stereotype of wo0o isn't anime suuper weird, and its not actually that fun to watch)
- Sword of the stranger
They aren't necessarily the best but almost all of them are easy to enjoy, the first 3 will appeal to anyone no matter what gender or genre bias.