Sean - I had the same problem living in NYC with a limited cellar.
Most wine storage facilities in the area (NYC, NJ, Conn) have a minimum amount they will store, usually around 10 -13 cases that varies from $1.80 - $2+ per case. NY Fine Wine Storage (http://www.nyfws.com/) is the only one that will take 1-2 case of wine at $2.20 per case with 3 months free storage.
NYFWS is the same ownership of Zachy’s wines but is a separate entity.
If you are looking for an alternative and have more wine to store, I would speak to Michael Mahle at https://domainestorage.com, a venerable establishment and I think he’s coming to the “NYC Rookies Unite”.
went through a similar exercise a year or two ago. Pricing can vary based on amount stored. also, what you’ll find is that some locations will charge more for storage but less for pickup/delivery or some will charge by box vs. 9L equivalents, etc. but pricing is all somewhat similar (unless you’re storing 50+ cases worth).
for what its worth i went with manhattan wine cellars and i’ve had no complaints (though it seems like all providers have their fans on this board minus the one that was flooded).
Once you are paying for storage, if it is a marginal cost by the box, rather than a fixed cost for the space, have a think through if it actually makes sense economically to store them. For some kinds of wine which can tolerate more temperature swings, and do not seem to go up in market value, it may more sense to acquire them in the ‘spot’ market rather than cellar them yourselves. Examples might include Sauternes or Ports.
Also, if you think you’ve outgrown your apartment storage, don’t just send the most recent overflow to storage. Go through everything, and pick out the stuff you are pretty sure you don’t want to touch for a few years. If that leaves you with space in your Eurocave or whatever fine, you’re still buying. What you don’t want to do is pay in/out charges for something you have offsite a few months.