Regarding the negative effect on taxi drivers, the economic consensus is that this is weaker than the positive effect on consumers. Generally as a society we prefer benefiting consumers over producers, as if all producers had monopolies and no competition, everyone's quality of life would be worse (producers are consumers too). There's a nice work from a few hundred years ago by early French economist Bastiat that explores the issue:
http://bastiat.org/en/petition.html.
That aside, their situation could be improved by the same general solution as other unemployment hardships: better welfare or some kind of basic income. This distorts the market less than giving taxi drivers an artificial monopoly and forcing New Yorkers to suffer allegedly sub-par service.
Regarding increased congestion, the standard solution is a congestion charge of some sort, applied equally to all non-critical passenger vehicles. This is what large cities like Shanghai and Singapore do (with massive taxes and/or licensing fees). Just because Uber contributed to the problem most recently, doesn't mean that their usecase is somehow worse than the cars that were already there. Increased use of such services can actually be a positive in the long term, if it reduces the time spent parking and the city's need to waste land on parking spaces, encourages carpooling, or increases quality of life of residents by allowing them to more easily get across the city. Increasing the cost of driving in the city via congestion charges or taxes will cut off the least important use-cases first (those that people are least willing to pay for), which is more efficient than arbitrarily banning ride sharing without data on the value it adds vs existing car usage.