Aside from breeding, the only time that I can recall using the Day-Care was in my Platinum Wedlocke, because I had just lost 2/3 my team to Cyrus and we were about to get to Sunyshore City, so even though it wasn't the most optimal choice, I decided on the Day-Care so I could get in some extra levels and not have to worry about doing too much grinding in areas I wouldn't feel comfortable at. Other than that, I don't use the Day-Care for leveling much.