What area in Rome to stay to be centrally located to everything

Not to sound flip, but have you looked at a map?

It depends on what you want to do during your three days.

We stayed in Pantheon area and thought it was perfect.

I agree about the Pantheon area being the most centrally located. There are some really good restaurants in the area too. But it can be expensive in hotels. There may be some more reasonable places on Air BnB, however.

We always stay within 3-4 blocks of the Ottavianio/San Pietro underground station. It's easy to get to from Termini by subway, and the Vatican museum is just 3-4 blocks. We can look down the street and see the entrance to the Vatican and St. Peter's Cathedral. There are a number of inexpensive B&B's in the area's apartment complexes.

We are taking the RS Rome tour followed by the Sicily tour. We have one night to spend in Rome at the very end before our flight home. We wanted a lively area, places to shop, places to eat, people watching, etc. We just booked here: https://www.hotelsancarloroma.com/en/index

When we do cruises in and out of Rome we stay in the Termini area. That is the transportation hub for the city. Termini is on the edge of many of the tourists site but still within easy walking distance. The farthest place - like a diagonal on a square - would be the Vatican and that is about 45 minute walk but take a bus from Termini. Being in the Termini area makes it easy to catch the train to Civitavecchia. The area has nice restaurants and convenient hotels -- Sonya, Aberdeen.

PS One other advantage to the Termini area is that if you do a lot walking in Rome and get tired it is easy to find a bus to Termini since many of the routes end there. Just see a bus with Termini on the front and get on. You know where it is ending. Same for the subway through it is very limited. All subway lines go through Termini.

Can not get more central than the Pantheon

Anything within 1/2 km or so radius from the Pantheon is the center of the city center.

Stay in the Monti district. Walk to the Colosseum, Forum and Palatine Hill. Metro stops very close and you can walk to Termini train station.

Depends on your budget. We stayed at hotel Smeraldo by the Campo di Fiore and its location was fine. The hotel itself was basic, but adequate. If you wanted a very nice hotel, the Grand Hotel de la Minerve by the Pantheon might suite your needs.

I made reservations at Hotel Due Torri for sister-in-law and myself for four days in May prior to meeting up with South of Italy tour. Hotel recommendation was from a long ago forum post. It is walking distance to most sites and attractions.

I booked an apt with loft right on Campo dei Fiori.
By map, nothing major is more than a 20 something minute walk.