Here are some synonyms for astronomical observatories, depending on the specific context:

General:

* Observatories (if it's clear the focus is on astronomy)

* Stargazing facilities

* Telescope facilities

* Astrophysical research centers

* Astronomical research institutions

More specific:

* Astrophysical observatories

* Space observatories (for observatories in space)

* Ground-based observatories (for observatories on Earth)

* Optical observatories (for observatories using visible light)

* Radio observatories (for observatories using radio waves)

The best synonym will depend on the specific context of your writing.