no lower than standard upper cabinets, 18" from counter to bottom.

if you leave it open like, the danger i see if you have pets in the house and tend to jump (cat) or fly (birds) not a good. Then if you have kids in the house and they are very mischief then also not good. Open Cabinet is good for grown adults personally.
Closed Cabinet at least it stays inside and if you have pets or kids, at least it will be scratches or stains nothing else and there is no danger to any china sets.