Planting both at the same time is ideal.

I agree that planting both at the same time would work out better as long as you take into consideration the eventual width that the hydrangea will get so that the clematis will not eventually be up under the stems of the hydrangea. It is normally best to plant the clematis at the outer edge of the hydrangea's eventual outer perimeter of growth so that the roots of the two plants aren't in direct competition. You can then lead the clematis into the hydrangea with a stick or garden stake.

You can plant them so that they are closer, but if you do, then the clematis is going to need extra care in terms of water and nutrition or the hydrangea will take more than its fair share of both.

Thank you SO much! The clematis has a trellis to climb so I'm not really concerned about growing it through the hydrangea. I just want them both to be healthy and happy.

Thanks for reminding me to take into account the hydrangea's eventual size. I would have been tempted to plant them too close together. :)