You'll be staying almost exactly where I live; here's how I do my daily running:
Walk outside of the apartment and head west toward the West Side Highway. When you get to the WSH, it's a nice double lane run/bike path that will take you all the way up to the GW Bridge if you choose so. From 16th street on the WSH up to 59th street is roughly 2.2 miles. If you want to do an easy 4-5, you can just turn around at 59th and head back.
But if you take a right at 59th (head east) and make your way toward Central Park, you can add some nice distance to the run and do an iconic NYC Central Park run either around the big loop (6.1 miles). It'll be a little challenging for you to hit the bridle path from the 59th street entrance without knowing exactly where you're going -- but it's doable if you look at a map before hand.
From 16th street on the WSH up to 59th, take a right head to the park and around the loop once, then back is about 13 miles. Longer than the 3-6 miles you want, but well worth it if you have the time.
If not, you may even want to go WSH and head south and run toward Battery Park (great views of Statue of Liberty).
Also, just to point out in case you're unaware, it's VERY easy to do your runs at night both on the West Side Highway and in Central Park. Both places are incredibly well-lit and if you do your runs later at night (let's say any time after 7:00 PM, it's quite peaceful). It gives you a rare opportunity to experience a sense of solitude while running in such a busy city. Especially in the winter, where in my four years here I've come to find most runners stay inside during the winter, you can really get the place to yourself if the weather is even a touch unpleasant.
Hope this helps.