Unfortunately, not really. The entrance to the site are a LONG walk from any kind of shopping area. Basically the closest place is on the far side of the ruins from the site entrance. Not that it could not be done, but if the idea is to cool down while taking in some shopping, then having to walk 1/2 mile in both directions in the heat kind of kills the plan. You would have to take a taxi. The only thing are the gift shops at the entrance to the site itself (there is a cafe there too).
We had train passes, we took the train from Naples to Pompeii, then continued down and had a late lunch in Sorrento which is really nice, then got back on the train and took it back to Naples. It took the entire day and we didn't get to see Naples.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013