If you do indeed go to Columbia, there are 3 or 4 things nearby that you might enjoy. Grant's Tomb, Riverside Church, St. John the Divine. The 1 stops at 116th, right there at Columbia.

If you visit Little Italy/Chinatown, you're not too far from WTC, Wall Street, 9/11 Memorial and Museum, etc.. They are 2 - 3 stops away on the subway, depending on which stops you decide to use

As for safety.. as the saying goes, there's safety in numbers, but common sense and awareness go a long way