The west coast of Basseterre should easily keep you occupied for 7 days. Pigeon Island is part of Cousteau Marine Park and has 7-8 separate dives sites by it's self. Piscine (swimming pool) is my top fav there, but Source d Eau Chade is unusual with two different hot springs and should not be missed. Unlike Dominica there is lots of life, coral, sponges and fish hanging around this hot spot. Tombant aux Carangues, is another nice dive on Pigeon. The wreck of the Gustavia is close by Pigeon, it is deep at 100', keel on the bottom at 130', but worth it if you like wrecks, better if you use nitrox or make it a deco dive. On the NW corner of Basseterre is Tete L'Anglais and Ile Kahouanne both good, but better are Gros Morne (shallow 20-70 with a cave), and Les Grottes a whole series of caverns (cool dive if you like caverns).
I would arrange a day trip to Sec Pate off Ile Des Saintes (fast ferries leave almost hourly from Pointe a Pitre if your Bassterre dive op won't go) it's a Real World class dive (between Guadeloupe and Ile Des Saintes). If you are not AOW/rescue or CMAS2 don't bother, no op will take you. Pain Du Sucre is also good there but not worth the trip alone.
I can't help with Ops, except to say last year I noticed a BUNCH of them in the bay opposite Pigeon Il and 2 in Ile Des Saintes while anchored there. I did grab a few Nitrox fills in Pointe a Pitre, but could not give an opinion on his operation.
