[camaraderie]

Not only Hell Gate but the entire East River must be approached to catch the tide "downstream" ...especially in an outboard powered boat. This is NOT sailing territory so with a new boat....you want to be VERY sure of the reliability of the outboard before you depart.
Best way to do it is to anchor or take a slip in Manhasset Bay/PortWashington the nite before and then plan to be under the Throgs Neck bridge and at Hell Gate at the ebb so you have the current with you all the way past the battery.
On the East River, use tide tables for New York. High tide at Hell Gate, Hallets Point, is 2 hours, 4 minutes later. SLACK tide only lasts for four minutes so you want to time things closely and NOT arrive early as you want the ebbing southerly current to help you. Stay OUT of the center of the channel and off to the sides where the current is weaker.
You can consider anchoring off the Statue of Liberty, taking a mooring at the 79th st. basin or perhaps going for a slip on the Jersey side at Liberty landing. You want a flooding tide to propel you up the Hudson so don't think about heading upriver against the current. Labatt's suggestion of a weekend passage is a good one. You need to pay attention to the current details but otherwise you should have a great trip and it is a thrill to go by NYC on your own hull!