The Nexus S is too cost prohibitive and powerful for this use alone. A custom device that is cheap and tough would be much better for this type of project. Maybe something low power that has great battery life? Maybe a Kindle like device?
The Optimus V on Virgin Mobile. $129 w/o a contract. Monthly plans start at $25, or if you want to go the cheap route, it has built in wifi, so you don't need a plan or use virgin mobile's service at all.
In fact, it fulfills of the OP's requirements:
* The device is a Nexus S with a custom version of Android where all apps are removed except a bitcoin client and Dropbox
The Optimus V can run android and has MANY custom roms, including some based on CM7, that run 2.3.4. All bloatware removed, with complete market access (access to dropbox, etc).
* The bitcoin client is based on existing clients, except also includes the ability to backup the encrypted wallet to Dropbox
Yup. Dropbox access is available. Not sure about bitcoin clients, but i'm sure someone can code something for android if it's not already.
* The user logs in to their Dropbox account to sync the wallet file
Check. Just need a bitcoin app built using Dropbox SDK.
* The user has one password to unencrypted the password file which they type in when the device is turned on
* The user has a separate, shorter password (a PIN), which they use every time they want to unlock the phone to send a payment
Check. You can either either a PIN or password when using a custom rom of CM7.
* The device would work over WiFi to connect to the bitcoin network
The Optimus V has wifi capabilities.
* The user could pay for 3G/4G internet access to be able to send money when they are not on a WiFi network
It doesn't have 4G, but sending bitcoins isn't bandwidth intensive. 3G will be perfectly fine.