How Far Is Central Park From the Financial District?
The short version
About five miles, and about twenty minutes on the train. From 17 John Street you walk a couple of minutes to Fulton Street station, catch the A uptown, and get off at 59 St-Columbus Circle. That stop sits at the southwest corner of Central Park, so you come up the stairs and the park is right in front of you. Rome2Rio clocks the Fulton Street to Columbus Circle ride at around 19 minutes, and trains run every few minutes most of the day.
59 St-Columbus Circle is served by the A, B, C and D on the Eighth Avenue side plus the 1 on the Broadway line, so if the A isn't there first, the C or D will get you to the same place.
If you want the east side of the park
Take the 4 or 5 from Fulton Street instead. Those run up Lexington Avenue and put you at 59 St, a block and a half from the park's southeast corner near the Plaza and the Grand Army Plaza entrance. It's the better choice if you're headed for the zoo, the Met, or anything along Fifth Avenue.
Rockefeller Center from the Financial District
Rockefeller Center is about four miles north, and roughly the same 20 minutes on the subway. Take the A or C from Fulton Street to W 4 St-Washington Sq, then switch to the B, D, F or M and ride to 47-50 Sts-Rockefeller Ctr, which comes up right at Sixth Avenue between 47th and 50th. The transfer at West 4th is across the platform, so it's an easy one even with luggage or kids.
What about a cab?
Figure 25 to 40 minutes to either one, and more at rush hour or when there's an event in Midtown. The subway usually wins on time and always wins on price. If you're going up for a show or dinner and coming back late, the A runs all night.
Worth knowing
Most people staying down here do Central Park as a half-day trip rather than a quick errand. Go up in the morning, walk the park, and come back down for dinner when the Financial District has quieted off. Weekends down here are calm, so the trip back is usually a seat-on-the-train situation rather than a crush.
Book your stay at 17John