Where is the best location to see the Lower Manhattan skyline? I know it is on the Brooklyn side of The Brooklyn Bribge but where exactly/ And how do I get there from the BQE?

Try riding the Staten Island Ferry - great views of the city.

Liberty Island State Park

Just carry on walking over the bridge.. you'll eventually, by following the walkway all the way round, end up on Brooklyn Heights. There is a long esplanade there with seats so you can sit and admire the skyline.

It's called the Brooklyn Heights Promenade. Get off the BQE at the Brooklyn Bridge/Cadman Plaza exit...though there may be an exit south of this that works just as well. The BB/Cadman exit will bring you out onto Old Fulton Street. Drive down the hill...it will bring you to Fulton Landing, a pier with spectacular views of the water & downtown. If you want to go up to the Promenade, just take one of the streets that goes up the huge, steep hill...I believe one is called Elizabeth Street? You should have no problems finding it from there...just go towards the water.

Take the Circle Line "sunset" cruise. Daylight as you depart, dusk as you turn around and head back, twilight or dark (depending on the time of year) as you go past the Statue of Liberty, and dark with the lights turned on all over (positively magical) as you return to the dock. The commentary along the way is informative and rather amusing. The Brooklyn Heights Promenade is fabulous as well.

The best view of the lower Manhattan skyline is from the Staten Island ferry.
When out in the bay you see the entire tip of Manhattan and, as a bonus, you can see up the Hudson and East rivers. The ferry is free and the ferry is easier to get to than Brooklyn from Manhattan. If you decide on the ferry when going to SI stand on the right side for a view of the Statue. When returning go to the bow of the boat. The trip takes about 25 minutes each way. The view from Brooklyn is fine but it doesn't compare to the view from the ferry.