Information about this lot
Political Boundaries
Government Agency
You can use this form to suggest uses that the community actually wants to see as concessions in this building:
https://www.nycgovparks.org/opportunities/concessions/suggest-idea
NYC Parks will consider your fantastic ideas and you should also share them as notes below and become an Organizer so you can connect with others to make the futures we imagine real! Keep in mind that NYC Parks isn't going to do your project for you.
Opening buildings costs money and NYC Parks' has a limited budget. HereĀ is a great guide to how to get money for your NYC Parks building stewardship project, created by the Center for Urban Pedagogy, New Yorkers for Parks and Partnerships for Parks: http://welcometocup.org/file_columns/0000/0613/improve_my_park.pdf. Follow the tips for "Capital Projects."
Getting your Council Member on board is key: they have money to give out every year via their discretionary budget; some Members allocate some of their discretionary money to Participatory Budgeting: https://council.nyc.gov/pb/. You can get involved to get the word out about the need to re-activate the building you want to steward.
The building might be landmarked. If it is, any work will need to comply with these rules: http://www1.nyc.gov/site/lpc/applications/applications.page
Pathways
News feed
Page 100 of the Riverside Park Master Plan dated June 24, 2016 Draft shows that the 1984 Master Plan envisioned a pedestrian bridge and overlook at 116th.

The photosphere shows an overlook, but what is below is the structure of interest.The photosphere also shows the grate that floods the tunnel with light. The photosphere does not show the barricades blocking the staircases leading down to the structure.
I believe its an access point for the West Side rail tunnel. Outwardly it looks very similar to structures at 109th, 105th and 102nd in Riverside Park, but inside its very different. I believe it did have functional bathrooms at one time. The popular name of the railway tunnel is the Freedom Tunnel. The name Freedom comes from a graffitti artist who used the walls for his works. This tunnel is very popular with urban explorers. There are many articles about this tunnel and many photos on photo sharing websites like Flickr.