I disagree, respectfully, with aiming for slack tide at midday at Hell Gate. I have made this trip several times and have always tried to ride a fair current as suggested by the offshoreblue rule of thumb I linked above. That means leaving Port Washington friday around 5 a.m. and passing under the Throgs Neck Bridge around 5:30.
Also, as others mentioned, bring a chart or have one on a tablet and be sure to pass west of Roosevelt Island.
Chiming in too late for OP, but this is correct. All the advice in this thread stating to time for slack at Hell Gate was not the best. Hell Gate is navigable even at peak current and it‘s a fun ride if you try to avoid the swirls and largest standing waves. You need to keep up your speed through the water to maintain steerage and time it to avoid going through next to large ships, whether slack or not.
OP should have timed for a high slack at
The Battery which would put them in Hell Gate about an hour or 2 before that (at City Island about 2-3 hours before) at the waning end of favorable flow. They would ride a southbound ebb current through Hell Gate and the East River, round the southern tip of Manhattan and ride the northbound flood up the Hudson as far as possible. (It‘s better to reach The Battery before the current turns than after, so err on the side of early, which is why I gave a range of time rather than being specific).
Monitor VHF 13 and 16 (set your VHF to dual-watch) and call any approaching ships/tugs or ferries (on 13 first) if concerned to ask how to stay out of their way or announce your intentions.
Hope all went well for OP. I’m sure it was an exciting trip.