We went to both Herculaneum and Pompeii, really enjoyed both, though Herculaneum is smaller. We went in late May and it wasn't too bad. We stayed in Naples (occasionally a bit dodgy but the hotel was nice); the Naples archaeological museum is good - bits there from Pompeii and Herculaneum on about two of the floors (steer kids away from the Secret Room though, hehe).
We found some nice small independent pizza restaurants in Naples, and some good gelato places. Lots of stray dogs about though.
Also worth a visit in the area is Capri, where you can climb up to the ruins of Emperor Tiberius's villa. Pozzuoli, where there is a reasonably well-preserved Roman amphitheatre and some temple ruins. Near Pozzuoli is Solfatara, an active volcanic crater with parts you can walk around (caution and adherence to barriers is essential and the smell is a bit interesting). Cumae is also interesting. Stabiae might also be worth a visit (that was the third Roman town destroyed in the eruption), as is Boscoreale villa (North of Pompeii where some of the treasures are kept - the rather haunting preserved cast of the dog is there).
We also climbed up to the crater of Vesuvius (you can get a bus a lot of the way, though the climb at the end was a bit arduous). Not sure that's the wisest thing I've ever done but it was amazing and I'm glad I did it.
If you do decide to go, I hope you have a really enjoyable time. x