Career wise NY might sound great; however you will get a wide variety of experiences in DC as well. Think about it. You will have the government option in DC, not NY. You will also have the consulting option because any large consulting firm as a DC office. Finally, you will also have the hospital option as there are many reputable systems in the area.
I think brand name has some weight when it comes to fellowships. I received a fellowship at WashU and I went to Florida but other fellows were from Michigan and Northwestern. However, Georgetown and GW are in the upper class of MHA Programs. So I don't think you have to worry about brand name nearly as much. Not to mention, MPH degrees can be drastically different from MHA degrees. One studies healthcare management while the other studies population healthcare management. Just my thoughts. PM if you have questions.