Your price range is going to be your biggest limiting factor here. I would be inclined to recommend University City, simply because of its proximity and amount of green space, but I've found few liveable properties below $300, and decent sized yards only add to the cost.
Within Philadelphia, your price range will limit you to areas of South Philly, Roxborough/Manayunk, and parts of the Northeast (perhaps a little too far from Penn though). These are all rowhouse neighborhoods though, so yards will be small, and likely paved over.
In the burbs, I'd take a look at Drexel Hill. Beautiful homes at affordable prices, and relatively convenient to University City. Its a part of Upper Darby, which generally isn't the most scenic place and has less than stellar schools, but thats what keeps the price down.
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