What's the best was to travel from St. Lucia to some of the other nearby islands?
Is there a ferry service? or ????

When I last visited st. Lucia there was a high speed catamaran ferry running daily to Martinique. By now there may be more islands connected that way. You can also take a regional airline (LIAT, Caribbean Sun/Star, etc) to various islands. These are generally not expensive, in the realm of $25-50 one way, plus taxes.

Any idea on where on the island the ferry leaves? How much it costs?

This link has the ferry schedules. Take something if you are prone to seasickness.

http://www.stlucia.org/planner/inter_island.asp

I would recommend a day trip to the Grenadine Islands. We did this excursion in '04 and loved it. It was running on a limited basis but I looked at the the link that MIM04 recommended and it states that Sunlink Tours is now offering it daily for $245 USD pp. It is a little pricey, but well worth it. It is an approx 1 hour flight with beautiful scenery of the island chain and then a day sail on a catamaran. Lunch and drinks were provided on the tour that we were on.