Are any parts of Lincoln Park in San Francisco more safe than others?

Not specifically. Just about all the parts of Lincoln Park in San Francisco are of roughly equal danger. As always, the thing that you want to consider is just common sense. If you are completely off the beaten track and out of earshot and eyeshot of any possible passersby, you are an easier target than if you are on a well-traveled trail. That said, most robberers don't like being out of their comfort zone either.