Pompeii, Herculaneum, Villas, & Naples Archaeological Museum Base

No reason to stay more than 1 night in Pompeii. Heraculeum can be seen in a few hours from Naples..
U do not mention your mode of transport when in the Naples area so I figure it is public transport. Train from Pompeii to Naples works then it is advisable to taxi to your destinations or walk a little. Naples is quite gritty and often times crazy with speed drivers and Vespa riders. Barely anyone obeys rules of pedestrian walks etc. That said realize your taxi rides could be seemingly reckless. That was our experience. But regardless we enjoyedNaples highlights. People either love it or hate it.
Best to select a hotel in a good neighborhood and spend a little to get the comfort and safety. RS guidebook mentions many that u should stick with. Always be super aware of your personal safety in the general areas u are visiting. Also include seeing the veiled Christ marble in the chapel. It is truly the most beautiful work of art I have ever seen.

Pompei is really not a very pretty place, although it's not seedy or unsafe. It is nowhere as beautiful as Sorrento, or as crazy and gonzo as Naples. The hotel looks fine, albeit lacking in character.

A Naples taxi ride is a thrilling and epic event. My most recent one last month was roughly equivalent to that Disney ride, "Mr Toad's Wild Ride." I was laughing and drenched with sweat after watching our driver dodge Vespas, Fiats, Pedestrians, Police officers, and anything else which happened to be in the street. Too much fun to even describe, and I was laughing out loud as I tipped the driver 5 Euros for the adventure as I related to him, "fantastico!" Staying in Naples was great fun, with amazing restaurants and wonderful people.

Sorrento is lovely, an easy train trip to Pompei and Ercolano, and it has really good restaurants.

You have two threads:

https://community.ricksteves.com/travel-forum/italy-reviews/in-depth-pompeii-area-5-days-where-to-stay

I would recommend just staying in Naples. You are traveling off-season. I would imagine a place like Sorrento, which has a lot of options for tourists, would be pretty sleepy that time of year. Pompeii town would be positively narcoleptic. Visiting these sights are only a small part of your day, you want to stay somewhere that has some real restaurant and activity options the rest of the time. The oft-maligned Circumvesuviana is actually very efficient for these sights and inexpensive. It takes no more than an hour to go from end to end, and drops you right by the main entrance to Pompeii. You’re making a mighty trade-off in overall enjoyability for a very minor convenience in travel by staying in Pompeii town (a very plain, uninteresting town by all accounts.)

In Naples, Hotel Bellini is well located, positively reviewed, and seemingly a good value.

I recommend staying in Naples. Granted I only walked through the town, but I did not find Pompei appealing as a place to stay.

If you want to travel on a much safer train than the Circumvesuviana between Naples and Sorrento, then book seats on the Campania Express train. It stops in Pompeii and Herculaneum as well. They have a hostess on the train and tickets are checked when boarding.
The trip from Naples to Sorrento costs about 9 euro. The Campania Express ticket office is in the Central Station, on floor - 1, right next to the Circumvesuviana ticket window. People with tickets for that train are escorted by the hostess down to the track where the train leaves and she stays with the group until the train arrives. She also boards the train and is very helpful.

The Campania Express is a good option for travel between Naples and Pompeii/Herculaneum/Sorrento because it's air-conditioned, less crowded, and monitored by train staff. However, it doesn't start running until mid-March, so that may not be an option for our OP.

We stayed in Naples for 3 nights last February and enjoyed it. 4 nights would have been better and with 5 nights you will have plenty of time. I would consider just staying in Naples and not moving hotel to Pompeii, esp. since it's not high tourist season and some (or many) things are closed in the smaller towns. We enjoyed the Hotel Piazza Bellini. They made us some good hot chocolate and we liked the included breakfast. We booked directly with them. We ended up with a huge 2 story room and we did find the stairs a bit much to tackle just to get to the bathroom which was down - two hands on the stair railing! We had no problems getting from the train station to the hotel on our own using the metro. At the end, we took a quick and inexpensive taxi to the airport.

We bought the 3 day pass with transportation (not sold at the Acheological museum when we were there, but they sent us around the corner to a Tabac) and used the metro in Naples and the trains to Pompeii and all they way to Paestum. We spent a full and very long day in Pompeii seeing as much as we could (it was a bit cold and we even had snow flurries one day in Naples) between eating pizza and warming up in the restaurant that was on site. Crowds were not bad at all and we were even able to do a fair job of getting photos with NO people in them. For me, that made Feb. a winner. Paestum was nearly deserted and I highly recommend it. With 5 days, you should have time. The Archeological museum in Naples was also wonderful, if a bit more exciting than expected because the strong winds blew the windows open and smashed windowpanes before they could be safely shuttered.