I only had a changing table with my older two. With the younger two it became very inconvenient to have a specific place to go to change the baby.
With the older two, I had the "classic" style of changing table that had the two open shelves under where you changed baby. I kept all the blankets there, as well as burp cloths, baby towels, diapers, wipes, and then any other miscellaneous baby stuff when I wasn't using it like the nursing pillow. When the babies were small enough it would still fit, I had a basket at one end of the top with a few diapers, wipes creams, etc. Anything that would likely be used at most changes. Once the baby was bigger, it dropped down to the first shelf to make room. Basically, you just want to make sure that anything you may need is within arms reach, so you can keep a hand on the baby at all times.
With my younger two, I basically kept diaper change stuff in the diaper bag, and changed them wherever, usually the living room on the couch or floor-and they were the two I cloth diapered, so I would usually keep a stash of diaper and wipes in the living room just because more than anywhere it was most likely where I'd be when they'd be changed.