Are you driving or taking a bus in? If driving, to save some $ park the car on the Upper East Side, free parking. Just mind the signs on when they clean the streets. Odds are you can leave it and not have to move it. Valet parking is ~50 per night with no in/out priveliges.
Going on a holiday weekend is going to be expensive. Also depends on where you want to be, down in the financial district vs midtown. Really isn't a bad place to stay, but for your first time I would recommend midtown, as its close to everything.
One thing I would do is check the size of the rooms. Some are only 150 square feet. I know you won't be in there that much, but may be a deciding factor. We liked the Waldorf, the Dream Hotel, but not sure if you can get them cheap as 300, especially on the weekend.
As far as what to do, just walk around. I'm not into the touristy things like going to the top of the empire state building or whatever, just seeing it from the bottom is good enough.
Free things to do: central park, 9/11 memorial, from there you can walk to battery park and see the statue of liberty. The plaza hotel is open to walk through, same with the trump towers and there is a bar to the left upon entering at the plaza where it is nice to have a drink, but $$. The bloody marys were $24 each. Also there is an italian market called Eataly that is fun to walk through, same with the Chelsea Market.
$: Museum of Modern art (25 adult, 14 student), empire state building (40$ per person), statue of liberty (tickets in advance), top of the rock (NBC building, 25$), skating at rockefeller center (think it is closed).
Dinner ideas: Colicchio and sons was great. Have always wanted to try Nobu for sushi but haven't gotten around to it. Sparks has good steak. Becco was amazing italian food.
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