I've had some good experiences buying plants online, particularly hydrangeas. A few years ago my wife purchased a hydrangea online as a gift for her mother, and later that year we visited and saw it thriving in the backyard. Worked so well I ordered one for my own mother and that worked out good, too.
The other thing about buying plants online is that some companies will guarantee a successful delivery, so it's always a good idea to check for a guarantee before you make an online nursery purchase. Nature Hills Nursery
has a policy that if a plant arrives in a damaged state, to refuse the order and they will reship a new plant. If there is a significant loss due to a low survival rate in a plant that was successfully shipped, Nature Hills Nursery
will replace it. That's a pretty good policy.
While it's always a good idea to visit a local nursery, it's not always convenient, especially for people with limited mobility or transportation options. Then there are people like my wife and I, who simply do not have a couple hours to spare (i.e. children) for travelling a couple towns over to a decent nursery and browsing around.