Is the public transportation from Manhattan Valley in New York City ok?

It's not ideal, but it's not awful. The only train that runs into it is the 1 which is the local train. But, you can switch to the 2 or 3 (express trains) at 96th street and be downtown in 20 minutes. Getting across town is a little trickier, but there are a number of crosstown buses that run from the neighborhood because of Columbia.