I would, without a doubt, choose house #1. When you child or maybe children someday, is older you really would want a good neighborhood. Also, living next to a playground and having a nature park behind the house greatly increases your quality of living, especially for your child(ren). When we lived in Columbus OH, we were within a block from a park and we had a huge greenbelt across the street. We went to the park all the time. When we were "too lazy" to walk to the park, we just went across the street and let Nathan run around. After OH, we lived in a different state in a not so nice area (the apt was horrible, too). We had to drive to parks because there wasn't one close. I absolutely hated that part!! Nathan really seemed to miss our walks to the park and just running around with other kids at the park. We just recently bought a house that doesn't have a park that close. Luckily we bought a house with a big swing set and a nursery in back of our house, so our son can have a little fun in our back yard and we also have no backyard neighbors!! We fell in the love with the house but if I could change on thing, I would want a park within walking distance.
If you choose to buy a home in even a semi-sketchy area, then chances are that the area will continue to decline and the home will most likely also decrease in value. You can either make it or break it in real estate. If you suddenly decide you want to move, it would be much easier in house #1. Your house would most likely increase in value and you could walk away with a nice down payment for your next home.
It stinks that the kids have to walk through the master but that is so small considering the other perks you mentioned. Public transportation is big but I would really consider quality of life. This is all just based on my experience.