The schools in northwest Greensboro have the best reputation. I think the Jewish temple might be up that way, but I'm not really sure.
Anyway, you can check school report cards at this site:
Advanced Search Results Page
It tells you how the kids scored academically at each school and how many incidents of crime and/or violence occured at each school last school year.
Many of the elementary schools are good, but that doesn't always mean that the area is good. Generally, 27407, 27408, 27409, 27410 are pretty good. As are Pleasant Garden, Oak Ridge, Stokesdale and Jamestown.
Florence Elementary, Southwest Elementary, Southwest Middle and Southwest High schools in north High Point are good schools. Your child can possibly go to those schools in parts of southwest Greensboro.
You should be able to find a very decent house for $200,000 in any of the cities I mentioned. Though home prices seem to be a little higher in Oak Ridge and Pleasant Garden. You would get more for your money in Greensboro, Jamestown and possibly Stokesdale.
I wish you all the best!