Matt offered a good suggestion. And while real estate professionals are proscribed from saying an area is safe or unsafe, what we can do is suggest to you that as the areas you are interested in are urban in nature that you walk about with recognition of your surroundings. Now if you ask me if I have encountered difficulties in Lincoln Park or Lakeview I can say to you truthfully that I have not in many, many years of living in this fine city. What I do know anecdotally from my cop friends is that because these areas are more affluent than many other parts of Chicago that some folks with questionable motives will show up looking for "easy pickings." Notice I am quoting neighbors who are in law enforcement. So, our response is to not provide "easy pickings."
By the way, your moniker suggests that you are a dog lover. Be cognizant that the presence of a pooch will significantly reduce your rental opportunities. I am not saying be free of Fido, but just know ahead of time that his/her presence makes your search that much more challenging.
By the way, Chicago is awesome. Welcome to my home and your soon-to-be home.
The Real Estate Lounge Chicago with @properties