I can't speak from any experienced as I have always lived here rather than renting but I would suggest that you look into the apartments that you have seen over by Ritter Park. This is a nice area with a lot of families and young professionals and you might be surprised by some of the rent prices you find. This would make it convenient to Ritter Park, downtown, I-64 etc and it is a great area.
Those who tell you that Huntington isn't safe have likely never lived here but they've "heard" and thus they "know." Like any city, Huntington has its areas where if you were walking through them you'd want to be a little more cautious but unless you were involved in illegal ativities, you would have little to fear. I walk to work everyday and my wife and I often walk downtown from our home. I see many other people walking, including children and young women by themselves, and have never seen anything happen to them or had anything happen to me.
This is a great town to live in with a lot to offer so I hope you enjoy your time here by taking advantage of the things we do have and by getting involved and connected to the community. Create Huntington now has a Marshall chapter that I suggest looking into to help you get to know Huntington.
Here's a link to the Tri-state Rental Guide as well as the rental section in the Herald-Dispatch. Hope this helps and let me know if you need anything else.
Herald-Dispatch -- Classifieds