I would start by comparing pricing for the appliances you want. Sometimes buying local works out to be cheaper. If that ends up being the case, I think it's a no-brainer. Supporting local businesses is always good, and should something arrive damaged, it tends to be easier to resolve that issue with a local business as opposed to an online supplier.

Buying online does often end up being cheaper, and if that happens in this case it's up to you whether those advantages are worth the price premium.