As a long time former resident of Brooklyn.
If you plan to commute and visit a lot of areas in Manhattan - you either spend 20+ mins walking cross town (from Manhattan hotel not central), taking cab for 20+ mins, or take the subway from Brooklyn for 10+ mins.
Manhattan lodging is easier for simply walking back to your room if late dinner or drinking if you stay midtown.
If you are comfortable with public transportation (24/7) you should/will have no problems. Aloft is a nice hotel and nice bar/lounge in the building. If it saves you money a good way to go!
When they say it is within minutes of Manhattan - most of the subway lines nearby have at most 2 stops (less than 5 mins) before entering lower Manhattan or Chinatown. One line goes over hte Manhattan Bridge.