My hubby and I dont drive and we spent 2wks in Sorrento in May/June, we also enjoy culture and sightseeing. We went everywhere by train, bus, and ferry - it was very easy to plan, you can get free timetables covering all three from the foreigners club. What we did do though was join the reps (free) walk about at the beginning of the holiday. It was a bit of a pain as they did take you into shops and at the end tried to sell you excursions (that we didn't buy) but it did give us an idea of where everything was.
We are planning to return to Sorrento next year as we still haven't seen everything even in Sorrento itself!! I must admit I wasn't impressed with Capri town packed with tourists, but you can go walking in the surrounding countryside which we did. We also went up to Anacapri, went on the very scarey chairlift to the top of Monte Solaro and saw the most fantastic views of the Bay of Naples. Have a wonderful holiday, hope you enjoy Sorrento and the surrounding area - we did.