I haven't personally been to St. Kitts (I will be heading down there once I finally get out of school), but my Aunt and Uncle have lived on neighboring Nevis for over a decade and I've had a lot of family go down to Nevis and you have to go through St. Kitts first. Their impressions were that St. Kitts is more touristy with quite a lot of things to do, and Nevis was slower paced and more ideal for a quiet, relaxing vacation. Both islands are extremely beautiful, just St. Kitts is a little larger and more populated. I highly recommend making a day trip to Nevis and checking it out.
As far as cigars go, I'm not aware of any shops on either island that I would feel comfortable recommending (no LCDH). My uncle gets all his cigars from one of the LCDHs on St. Maarten. You might check with the hotel you are staying at and see if they carry any at the bar or can give you a recommendation for a shop on the island.
