You can say it your way too - but we would say it more like: --Once I was at a small private observatory and could watch Andromeda nebula. ...why at vs in? While you can go into the observatory, you are there at the observatory.
--Once I visited a small private observatory and watched the Andromeda Nebula.
Also nebula would be capitalized when saying Andromeda Nebula because it's a proper noun (the full name of something).
and .. it's been reclassified it's actually now Andromeda Galaxy (not a nebula).