In MA it takes 2-3 business days to get a marriage license.
We understand that and they have an option for one day weddings. Just paperwork and money.
There are many beautiful parks in Salem - Salem Willows, Winter Park, Washington Square, Gallows Hill, Forrest River Park. Not sure if any of them have restrictions. The National Park service owns the area around the Friendship on Derby Street but you may be able to take pictures there without a fee. I was married at Hamilton Hall on Chestnut Street, a beautiful venue with a small park across the street but I rented the facility for the day and had guests. Not sure if they would be open to just a ceremony but worth a call. You could also try the Salem Athenaeum, Peabody Essex Museum, the Old Town Hall or the House of Seven Gables but they also will likely charge a fee even for short use. Good Luck!
I did not realize they had the 1 day option. When my friend looked a year or so ago they could not get a fast one. That being said I would do the Washington square. I got married across the stree but took pictures there. The gazebo is beautiful. Not sure the name but there is a nice grassy area right by the freedom and that would be pretty too
In front of the Custom House. This is on Derby Street and facing Salem Harbor. Google the Custom House in Salem MA and I think this is what you are looking for.
Click on each tool to see a sample.