I'd avoid Kansas City, KS. If you're looking in the KC Metro, you could probably find quality housing on the KS/Johnson County area (Overland Park, Shawnee, Lenexa, Olathe, etc) but they do have higher property and payroll taxes (iirc) than in MO. You won't get as much house for $150k as you could probably find on the Missouri side.
I just bought a house in July and was looking all over the KC Metro really, and found that $150k went alot farther on the MO side than the KS side in most cases.
I live in Blue Springs, a suburb ~ 20 minutes east of downtown with excellent schools. Lee's Summit is just south of here, again, excellent schools. Both are (IMO) nice cities to live in and relatively low in crime. Grain Valley is just east of me in Blue Springs, it's a smaller town and growing fast. Figure an additonal 10 minutes to get to downtown if you choose there. Lots of new and newer houses there and the price is right.
I can't speak for north of the river (Liberty, North KC, etc) since us south of the river folk don't venture north of the river much (at least that's the stereotype).
I'd suggest getting in touch with a real estate agent and telling them your requirements and having them show you some various areas. That's their job, afterall. I can put you in contact with the one I used, which I highly recommend.
Hope that helps a bit.