I have seen a lot of literature lately suggesting that people have their downspouts lead into a rain garden. Search "rain garden" and see what comes up. Maybe that will work for you. I'm not so sure about the rest. Do you have a french drain around the edge of the house underneath that gravel?

Thanks for the reply. I researched 'rain garden' and feel it is too much work for me at this moment. I don't see the french drain surronding my house. For this project, I am thinking using the stone walkway I am planning to build as a drainage path. Do you think it is a good idea or not?

Thanks,
J

My husband and I built underground draingage at our downspouts. It was one of the best things we did for erosion control around our home.
It was alot of work but well worth the effort.
When I go out side and see the water moving down to the bottom of our hill instead of creating a stream effect from our downspout down the hillside I feel really glad that we did it.

We bought all our supplies at the big box store Home Depot.
Looks like you would benefit from under ground drainage.

Stone path could work. Make sure everything grades so that water drains away from the house. It sounds obvious but somehow gets overlooked sometimes. The stone needs to be set in something like gravel or stone dust or it will sink in over time. You might want to put edging around the stone path to hold in the gravel or whatever that underlays the stone steps. There are concrete non-skid stepping stones you can buy now that actually look pretty good. The drainage kit Lovely mentioned sounds like a great idea. You can also buy pre-cast drywells to bury in the ground into which that down spout could feed - but research first so that you put in a system that can handle whatever your volume is. The middle area could be planted with grass seed but it will need to be covered with grass starting blankets which are readily available at big box stores and are usually green in color. You could make a pea gravel path instead of grass also. Do all grading and hardscaping before you plant anything. My brother made his own french drain with perforated pipe and gravel, etc. along the edge of his house and has it discharge into a shrub bed downgrade. It's still working well a few years in. I hate to say it but I think that whatever option you use will involve digging (I hate digging but it's unfortunately an all too necessary task much of the time). Good luck. As annoying as this all seems you are being very wise to address it now before it becomes a big problem. Good luck!