I hope I can be of a little help... I'm not totally familiar with all Renton neighborhoods, but I do live a few miles east of the Cascade neighborhood. Where I live is Fairwood, technically unincorporated King county, but with a Renton address. This area is really pretty nice, all residential, great for families. I've been through the Cascade neighborhood a few times and I think that would be an okay area too. However, a long time ago I lived in an apartment near the NW corner of the neighborhood that I wouldn't recommend.
Benson Hill is so-so. SE of Cascade, east of Boulevard Lane Park is nice too, a friend of mine grew up there.
And you're right, Skyway isn't that great. It's been a while since I've been over there, but when I was looking for the house my family is now in, that would have been near last on my list of places to look!
Will you get a chance to drive around these areas before you move? That will definitely give you the best feel for where you'd like to be. I hope this helped! Good luck!