For Pompeii I would stay in Naples - there is a train that takes you directly to the site, thus avoiding the horrendous traffic and rapacious taxi drivers. And Naples itself is full of treasures. All the hotels on the Amalfi Coast charge rip-off prices though it might be slightly cheaper in May which also happens to be a great month to visit, before the summer hordes arrive. Almost all the hotels are vertical and compressed, compromised on space, especially their grounds and pools. Sireneuse pool is particularly pathetic. Beaches are non-existent. By all means rent a car if you have nerves of steel. The main road is narrow, with a brick wall on one side and a cliff on the other. Don't meet a bus coming the other way. Speaking of which, buses and ferries are the best way to get around here, ferries especially nice.