I don't have a lot of details about your situation, so take this advice for what it is worth. But it sounds to me like:
You are currently an administrative assistant, and have been in that position for some time. You have been offered a position as an analyst (I'm not sure what type of analyst) within the same company, which is a big step up. You are in NYC, and your husband has applied to Columbia business school. If he gets into Columbia, everything is great, you can stay in the job while your husband is in school. If he doesn't get in, there is a possibility he will have to leave NYC to go to school, at which point you will have to decide whether to go with him, or whether to stay at your job in NYC for awhile while having a long-distance relationship.
I guess I have two questions:
1.) Has your husband applied to other NYC grad school programs?
2.) Does your husband have a good chance of being accepted at Columbia?
Regardless, my advice would be to take the job, for several reasons. First, you don't know what is going to happen with your husband's grad school options. This is a big opportunity for you. Your husband won't be starting grad school for another full year, which means you will be in this new job for a whole year before there is even the possibility that he leaves. That is a lot of time to work at one place, and I think the opportunity is too good to pass up.
Additionally, I don't think leaving the job after one full year of working there would be terrible. It sounds like you have been with this company for awhile and have good relationships with the people there. If your husband doesn't get into Columbia and is leaving NYC, you can tell them the truth--that he has to leave for school, and you want to be with him. I think most employers will understand that, particularly if you give them ample notice.
I think that the jump from being an administrative assistant to an analyst is a big one, and if you pass up this opportunity you are hurting your career and your future academic options. You mentioned wanting to go to B-school. I know that most good B-schools put a lot of emphasis on work experience. You will be far more appealing if you have experience as an analyst than if your only experience is as an administrative assistant. Additionally, if your husband does not get into Columbia and you decide to follow him, wouldn't it be better to have a resume that shows upward mobility within the last company you were at, and experience as an analyst? With that, you will more likely be able to get another analyst position. If your resume only shows administrative assistant experience, it will be more difficult for you to find something other than administrative assistant work in the new city you move to.
The fact that you don't want to stay in NYC super long-term doesn't change my advice. I think that a year or two or more in the analyst position will help you a lot, and then when you leave you will have better options. Lots of people move to NYC, work there for a few years and then leave. It's not something I would worry about.