Ah, I see now! Okay, at $300, it's going to be a bit difficult to get what you want really close in, but it might be possible. A quick look at the MLS shows a few 3/2's in MLS areas 1A, 1B, 6, and 7 (those are all pretty close in to downtown) in your price range - close in to downtown, built from 1935 up to 1981, a closer inspection would be in order to see which, if any, fit with what you're describing, but they're out there.
If you add in MLS area 4 (UT and north), quite a few more pop up that were built mid-last-century.
Shady Hollow is another possibility, as well.
As for schools, you might want to check out
GreatSchools - Public and Private School Ratings, Reviews and Parent Community to get some parental feedback on the various schools, and also remember that a school that is great for one kid might be a disaster for another, and vice versa.
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