It really depends on how much commission is being charged by the music shop, and what they're expecting to get for it.
Remember that eBay charges significant fees for sales:
10% is taken right off the top by eBay itself (this includes the TOTAL sale price, including both item and shipping costs. For example, if you sold it for $3900 and $100 shipping (or $4000 with free shipping), they would take $400 in fees.
Then, add in the 3% that PayPal takes, and that's another $120.
Let's say that you sell it for $4,000, all in. You would lose: $400 from eBay, $120 from PayPal, and then you'd have to factor in your shipping cost. Let's say that it costs $100 to ship.
You would net: $4,000 - $400 - $120 - $100 = $3380.
You lose $620 off the actual sale price.
Reverb.com is another place to sell, but in my experience you don't save THAT much over eBay. See here for a breakdown I did on the sale of a $350 oboe on Reverb compared to eBay:
http://clarinetpages.info/smf/index.php/topic,1285.msg8261.html#msg8261Something that I've always considered but have never pursued, is selling it to a local university. I am very close to UCLA, which has an extraordinary collection of instruments. I don't know how their purchasing department works, but if your local university needs a contra alto, they could be an option. High schools and middle schools will not have enough money or use for something like this, so no need to waste your time with them.
Craigslist might be tough, as again it's an extremely niche instrument and there simply aren't that many buyers in the market at any one time.
eBay and Reverb will get you the largest audience. But do remember you're losing a significant of potential profit on any sale on these sites.
If the local music shop takes LESS than 13% commission, then it might be a good option. I've personally never done that before, but it could work.
I occasionally sell instruments on commission, but I've never tried to sell something like this, it's always been popular, liquid clarinets.