I would like to stay in or around AMS for 3 mos.Which areas could I rent a flat for 600 euros or less? Safe. No car. I will have a bike.
A flat or a room? I would say that 600 euro for a flat is quite impossible as a room in a shared flat is mostly 400-500 euro itself... And not even in the centre of the city...
Try surinamplein, my friend rents a flat there. It`s close to the center
You might also consider Amsterdam North. It's very close to central station, and is currently 'up and coming' so you get far more for your money still. In comparison with other cities, there aren't really any no-go areas within the city ring, so I wouldn't worry about safety. Everywhere within the ring is also served well by public transport.