This seems to be called both Beechwold Park and Beechwold Nature Preserve in the Columbus city sites and new nature preserve booklet, in which it is featured. This is a really lovely little area...

Beechwold Park is a cute little ravine in the middle of Old Beechwold. However, walking around the neighborhood will be a more interesting trip than walking down the ravine and out the other side...

Beautiful park in a ravine in the middle of a quiet neighborhood. No real amenities- no dedicated parking, no playground, etc. But a lovely place to walk and relax.