I am looking to plan a VERy budget friendly trip to DC/NYC for either October or March. We have train tickets to go from DC to NYC for the day so that cuts down on that cost and will be staying in Bethesda, MD and the hotel offers a free breakfast and parking and is about a block from the metro. I would love any advice on how to make this as budget friendly as possible (we will be going Thurs-Sunday) and if there is a better day (Friday or Saturday) to visit NYC. I'd also love opinions on which month would be better to visit both. We have only been in March to DC and I know the weather was all over the place but wasn't sure about October? Thanks in advance!