Is there a place (or places, but hopefull just one) where I can ship
the following items to be recycled in an environmentally responsible
way?

Portable phones, wristwatches, printer cables, AC adaptors, printers, modems.

Office Depot will accept one item per day, but you must bring the item
in person rather than ship it:

"Now through Labor Day, bring your unwanted PC, laptop, printer,
handheld, cell phone ? or any other qualifying product ? to your
nearest Office Depot. We?ll send them to HP?s recycling plants where
they?ll be processed into material that will be used to make new
products. Bring in products made by any vendor ? not just HP. Best of
all, this service is provided absolutely FREE of charge."

http://www.officedepot.com/promo.do?file=/promo/pages/recycle.jsp

This organization in California will certainly be able to refer you to
someplace close to you.  They are a highly successful computer and
electronics reuse/recycle setup:

http://www.crc.org/