I travel solo all the time and am from Connecticut.
You will have no problem traveling solo to the city. Its done all the time by all sorts of people for business and pleasure as well.
I do not use the subway EVER !! Did it a few times as a kid...and that was a long time ago. If you really want to experience it go ahead...but I couldn't be so bothered !!
Get your self a map--either copy it off the internet or buy one so you can sort of plan what you really want to see.
I suggest Central Park...you cannot possibly see it all---but see what ever side you can get to. its so special.
This area also has some of the great museums of the world.You cannot see everything --but if you do your homework beforehand --there might be an exhibit that is of interest to you !!
The Theatre District area is the best. You can probably pick up some tickets..reduced of course to see a afternoon showing. This you can check out on your computer at this time to see what may spark your interest..but just viewing all those Marquees always brought me joy.
Radio City Music hall---http://www.radiocity.com/
Empire State Building--http://www.esbnyc.com/
Take a ferry around the Liberty Statue--this is another of my loves....several different choices of boats even dining ships.
Leave for New York in the morning right after PEAK trains. It will be cheaper.
Somewhat plan your day for the three or four places you really want to see.
Plan to start in one area say Central Park and the museums on the East Side for first half or head to the ferrys if thats one of your fav's--then work to Times Square which is better to see more late /to dark. ( at least I think so )--unless you get tickets for a show--then you'll need to build your day around that
42nd street is closer to Grand Central Station---so ending in the area makes sense----------
Avoid travel during rush hours during the week days around 5pm to 6 or 7pm. Try to be comfy in a restaurant having dinner and a cocktail.BB Kings restaurant and Jazz Club is in this area if of interest to you.
Times Square--This is the place EVERYONE wants to see.
Edited: 3:40 pm, September 08, 2012