Welding shops are a good bet. They usually trade out a full one for an empty one. If you want to keep your tank, you might check a fire extinguisher company. They typically can fill your bottle so that you can keep it.
If you were planning to keep your bottle, post a pic of it. You shouldn't need an adapter. Do you already have a regulator for it?
there are a few liquor stores that will fill it. Home brew mart has a list of them. I go to liquor locker on Morena Blvd, its about $16 for a 5lb fill. Air-gas will do an exchange as well. The advantage there is that you will be getting a full 5lbs instead of 4lb or so from a typical fill place. disadvantage is that they charge whatever they want (I've had them try to charge me anywhere from $18-$29 for a 5lb tank).
I also use Liquor Locker, I think it's like $3-4 per pound but it's close to my house. Beer King on Clairemont Mesa (behind the Guitar Center & Arby's) used to do it but I don't even know if they're there anymore.
Just thought I'd revisit this thread and post something current. I get my bottles filled at Keg n Bottle on Massachusetts Ave in Lemon Grove. $17 for 5# and $22 for 10#. Price has varied depending on who's working. They prefer frozen bottles and they do not use a weight scale; just a straight fill till it won't take anymore. Used to go to Beer King on Shawline but I don't think they're there anymore?