Take the LIRR to Syosset station. From there you can take the CSHL shuttle van, Google the schedule. There are regular walking tours, you can Google the schedule for those as well. Alternatively, email and take appointments with scientists.
You are welcome to visit CSHL, and may request a tour, don't know if you have to pay though. I am a researcher at CSHL, and usually there are special events for general public.
Visiting and meeting with the researchers is not done without a prior appointment. They host many conferences during the year. However the library is open to the public.
There is a LIRR station close to the lab. I would strongly recommend email the people before visiting coz they might be busy or might not be there. There is a guest parking lot as well in case if you want to drive.
i recommend looking online for a public conference, but otherwise, I'd start by visiting information at Grace Hall.
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