LS,
Who told you that the world should be free from suffering?
As an empathic human being I wish that it were. As an atheist I know that there is no divine plan and that things just happen, the universe is oblivious to it's effects on us. If an asteroid hit the earth tomorrow and wiped out all life it did not do that on purpose we were just in the wrong place at the wrong time. If I believed in a biblical creator god then that asteroid has to be part of his divine plan and hence the suffering was caused by god.
Do you find any value in suffering?
No, that is not to say that people don't overcome all manner of adversity and emerge stronger. In spite of this it is not something I would inflict on anyone or anything by choice.
Do you think it is possible to experience all the beauty and goodness and pleasure the world offers without also experiencing the bad? Isn't good only good because we know what bad is? If there was only good would it really be "good"?
That is a good question but you really need to define what you mean. Firstly, I would differentiate between the 'bad' that is part of nature and 'bad' that is a result of unnecessary human activity. Could we eliminate human evil and still know what good and bad was? Probably yes, the vast majority of humans do not commit acts of evil, not because of god or hell but because of empathy. Could we stop natural disasters and still know good from bad? Yes, we do it all the time, If you don't live on a hill and are not knee deep in water twice a year it's probably because we have flood prevention engineers mitigating that natural disaster.
If you where God and could eliminate suffering what would the world look like? Or conversely if there was a loving God what should we expect the world to look like?
Much like it does now but without all the natural disasters, starvation and psychopaths and much more empathy for humans. If there were an omnibenevolent god then that would be the only sort of world it could design!