Unfortunately, the bacterial pathogen that causes Lilac blight, Pseudomonas syringae, is known to affect a wide range of ornamental plants including hydrangea. You may want to remove the impacted plants and wait a season before putting in new plants that could be a host.

"The bacteria overwinter and persist in cankers, along with asymptomatic bud and twig tissue. In presence of water and warming temperatures, bacteria multiply and may ooze from infected tissue. Wind-driven rain, insect, or mechanical pruning spread Pseudomonas. Bacteria enter the plant through flowers or injury."

https://www.purdue.edu/fnr/extension/pseudomonas-syringae-pv-syringae-on-lilac-and-other-woody-ornamentals-landscape-report/

http://plantclinic.cornell.edu/factsheets/lilacbacterialblight.pdf

If you remove the infected plants and allow some time for the area to rest and recuperate, you should be able to plant Hydrangeas there. Before you do consider doing a soil test, taking a look at light levels, and think about how you'll water new plant material in that location. That way you'll be set up for success when you do put in your new planting. 

https://homesoiltest.msu.edu/

Stressed plants that are not planted in the proper location, aren't receiving adequate fertilization, or are not watered appropriately often lead to bacterial problems such as this or other issues. For whatever you decide to plant, avoid wetting the foliage with overhead watering to minimize splashing of the bacterium on to the host plants. Prune plants during the dormant season to allow for increased air circulation through the canopy while avoiding disease spread. Also be sure to space your plants according to their label.