Anyone know a cheap big space in NYC that would be great for a wedding?

Hmmmmm. That’s a tough one for NYC, in any season. You might want to check out some of the restaurants in, say, Little Italy. They tend to have Private areas and then they’ll cater for you as well.
Honestly, however, I don’t know that you’ll be able to keep it under $1000, especially going with a restaurant space and having them cater, which still might be your cheapest idea.
I don’t know how cool you are with the outter boros, so check out restaurants in Astoria, on the water in Red Hook, etc.

Good luck, and congratulations!

Are you planning to rent a space, and have someone cater the event? It’s generally more cost-effective to choose a restaurant that does events like this—the cost of the space is folded in with the cost of the catering. Also, if you rent a space, and have catering done by someone else, then you’ll be responsible for renting tables, chairs, tablecloths, and cutlery. And that gets expensive.

Are you getting married in a church? If not, do you mind churches? Many have banquet rooms. I would also check out organizations that have space and need money, generally, like Boys and Girls Club, things like that. Daughters of the American Revolution, the local YMCA, Knights of Columbus. For $1000 it’ll be tough, and I wouldn’t count on getting a space in Manhattan for that price.

I reiterate the restaurant suggestion. If you’re interested going outside of Manhattan, there are also great restaurants in Astoria, Queens, which is totally accessible to Manhattan, and not so hip that the prices are insane.