Your model number will be one of the following if it's a console:
If it's a chairside, the model number will be one of these:
If you can't find a model number on the back of a console cabinet, the model number is also usually (but not always) stamped in dark ink directly on the chassis. It's plainly visible on the gold chassis, when the radio drawer is closed. If you can't find the model number, I can post pictures of all the models in this range, and you can pick out your model from them.
If your radio is the 12H090, which is the most common of this range, the cabinet must be in rather good condition for it to be worth any reasonable amount. The critical thing with this particular cabinet is that the faux woodgrain that makes up most of the exterior is prone to failure if it hasn't been treated with kid gloves for the last sixty years. The loss of the woodgrain lowers the value dramatically.
Sadly, as Paul mentioned, they're not worth much. Which is a shame since they're supremely useable radios, when restored. I have a 12H090 and a 12H092. The 92 is in storage, but the 90, which works as perfectly as it did when it left the factory, is listened to on a daily basis.
I'm not sure about the best way to sell it, but the worst way to sell it is on eBay. Something this large can't be easily shipped, so your customer base shrinks to only those near enough to you to pick it up. Even then, most people won't bid on it if it's more than $75 or $100 (IF it's in great condition). Most folks though, have the same problem you're having... They just don't have room for something like this. If you try selling it through some local channels, you may be able to get more for it, though.
My advice would be to have it repaired, make a place for it in your life, use it as it was meant to be used, and cherish it as it's first proud owners once did.