Inbound from Brooklyn, you might want to try Dean/Bergen Streets instead of Flatbush...they actually have bike paths. Coming home, if I take the Brooklyn Bridge, I cut up Dean and merge w/Flatbush right below Sixth Avenue. If you live south of Flatbush, you might want to try some of the other name streets...I go all the way to the other side of the park, and there are a couple of streets that minimize/maximize the climb up the Slope, depending on how I'm feeling. I almost always take Flatbush in the morning...the first leg of my commute includes the long climb uphill through the park, so I like to make up for that by cruising down Flatbush, where I can really pick up speed.
I'm of two minds about the bridges...I like the Manhattan, because it's a bike-only path, but the Brooklyn is nicer aesthetically, and leaves me with a straight shot across Chambers to my uptown swing. When I work on the east side, though, I always take the Manhattan, because the east office is at Broome and Mercer, which is easy to get to via Christie or the Bowery. The real drag for me on the Brooklyn Bridge is the pedestrians. I actually have and use a bell on my bike, and I'm ringing it almost constantly on the Brooklyn Bridge...especially during the descent, where I should be flying instead of braking for the clueless!
Here's my suggestion for the uptown trip on the West Side: Take Hudson Street. Despite the tunnel approach at Canal, it moves quickly. If you stay on the left, you'll miss most of the traffic, as tunnel traffic exits and enters Hudson on the right. You'll also be in position to be in the bike lane, which starts just north of Canal and extends to 14th Street, at which point it becomes Eighth Avenue, which is usually pretty empty. (My commute stops below Fourteenth, but I've ridden Eighth a lot and never had any problems.) This'll get you out of that West Side wind, which can be a killer.
I take the West Side bike path at night, though, because I like to build up a good head of steam before I get to the bridge, so that I kep my average speed high enough that I'm home in under 30 minutes. The West Side bike path and the Prospect Park loop are where I can make up time, coming home, that my tired legs have lost on the bridge ascent and the climb up Flatbush.
I am such a NYC commuter geek.
(As long as we're throwing in restaurant recommendations: Indian Bread Company on Bleeker Street makes amazing sandwiches: curry on naan bread pressed flat and heated like panini. It's a little expensive for everyday lunch- a "naanini" and soup is $10- but I've been eating there as much as I can afford to, it's that good. Bleeker just east of Sixth.)