I like the Embassy Suites Battery Park.
Two blocks from the subway, next door to the World Trade Center, and walking distance to Battery Park where you catch the ferry to the Statue of Liberty and Ellis Island.
It will probably be more than $200, but keep in mind that the price INCLUDES cooked to order breakfast for everyone each morning.
If you were to pay for a family of 4 to eat breakfast at a Manhattan hotel, you would probably be about $50 anyway.
If cost really is an issue, stay in New Jersey near Liberty State Park, and take the ferry to Battery Park each morning, and use the metro to tour around. If you go that route, be sure not to miss the last ferry back to NJ at night...then you are screwed.
Hope this helps.