I'm not a big fan of rock mulch, other than in an occasional rock garden - hydrangeas aren't rock garden plants. Stone used for mulch doesn't decompose or add any nutritional value to the soil as you would have with an organic mulch. Without the organic matter there is no environment that would attract living organisms needed in the soil to benefit the soil structure and add the nutrients needed naturally for plants to thrive.
The lighter shades of stone can reflect heat back up towards plants, which may be harmful, then there is the maintenance issue of all the leaves, twigs, debris, weed seeds that will fall into the rock and need to be cleaned up....I'd stick with something organic, something that was once a living plant or piece of living plant :) A new bed may take some attention the first couple of years its in place, upkeep becomes less over time if you don't let weeding get away from you.

Thank you

I have river rock around my landscape and would like to know if I can dig a hole and plant hydrangeas?

Hydrangea roots are normally found in the top 4" of the soil. As long as the river rocks are small enough, not too "concentrated" in that area, a little spread out.... letting plenty of soil in between rocks, then that will not prevent the roots from growing in the area and will allow the roots to find soil nutrients... then it may be ok.

Just a fyi: I would not use river rocks as mulch though. One of the uses of organic mulch is to protect the roots from high/low temperature extremes. As it decays, it also provides nutrients to the plants. Rocks do not help much with either. Moreover, rocks absorb heat during the summer months and, just as the hydrangea is about to get some respite from the sun/heat at night, the rocks then start to release the heat. That stresses the plant. I would not use river rocks as mulch on newly planted shrubs until after the plant is established in the garden and has a larger rot system.

If some of the rocks' materials can release lime, you may need to counteract that.