I was thinking of catching a ferry over to Capri the day we arrive in
Naples. (We arrive at 1:30pm) and spend 2 nights there and then
spending the last 3 nights in Sorrento. Or would you spend all 5
nights in Sorrento?
Cindy, we've actually done the same thing so your plan is fine. You'll need to transfer from either your plane or train to Naples to the port to catch a ferry to Capri. The island is a better experience, IMHO, if you stay there versus day-trip it: you'll be able to take advantage of the golden hours when the mass of day visitors have yet to arrive and after they've departed. You'll have no problem at all finding enough to do with just one day, in fact will not be able to take full advantage of what Capri has to offer.
Skip the Blue Grotto (we did): not worth the time or money for the few minutes you're actually in the thing. DO try to do some exploring to some points away from piazzas on the island (the hike up to Villa Jovis highly recommended).
Ferry schedules for Naples and around the region here:
http://www.capri.net/en/ferry-schedule
There (Sorrento) we could do a day trip along the Amalfi Coast and hit
Pompei one day. Any suggestions on other day trips?
3 nights in Sorrento will only give you 2.5 days: 1/2 day for Sorrento itself; one day for Pompeii and one day for the Amalfi Coast. That's really all you'll be able to manage in that amount of time. Pompeii is HUGE so you could spend the lion's share of the day there. It will also be hot and wearing so you'll likely just want to go back to the hotel and collapse when you're done! Take the Circumvesuviana commuter train from Sorrento: takes about 30 minutes and tickets are dirt cheap; remember to validate them before boarding the train, both directions, as checks are not uncommon and fines for unvalidated tickets are high!
http://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule
You'll want to get off at Pompei Scavi - Villa dei Misteri station, right in front of the main entrance. Human guides, if you want one for touring the scavi, may be hired at the entrance to the excavation or do it independently with a guidebook (we did).
Also, does anyone have suggestions on where to hire a driver for the
day?
Sorry, no help there as my stomach could NEVER have handled the coastal road in a car or SITA bus (severe motion sickness 🤢) so we did our moving around by ferry. I'm sure someone else will have a good suggestion, though!