Hi there, We lived in Oak Ridge for 2 years and Knoxville for 6, before moving away last fall. What sort of place are you looking for? I'd say yes, it's possible to get a few acres. Downtown has really grown in the last few years and has gotten pretty nice. As far as crunchier areas, probably the Old North neighborhood, or Park Hill. Both are east/northeast of downtown and I'd say about 30 min from Oak Ridge. Also some parts of South Knoxville (south of the river and downtown), although I'm not as familiar with that area.
Oak Ridge, and out toward Oliver Springs you might be more likely to find some acreage. Also some areas of west Oak Ridge are nice and have sizeable yards, at least. Plus there are several green belts and the Oak Ridge Reservation that lots of homes/neighborhoods back onto, so there's green space available for roaming at least.
Also in Knoxville there's a really great AP community with an API support group that meets every month on the west end of Knoxville. PM me if you'd like more details!
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