Golden Oldies first Roman Adventure: advice sought!

If recommend booking a tour of the Colosseum that includes the Forum and Palatine Hill. I found those two far more interesting that the Colosseum.

The Vatican and the Colosseum are a bit apart from each other, so you will need to find some middle ground. We took the Hop-on-Hop off bus on our first full day in Rome; it was a great way to get oriented to the layout and see where things were. Both places you want to see are major tourist attractions, and you should get tickets from a reputable ticket seller well before traveling. I think some people have had trouble with Viator and Get Your Guide tours being canceled at the last minute. Best to go to the official sites. You really should get the Rick Steve's Rome guidebook, he has so many great tips and information.

My trick for finding hotels is to go to Google Maps and have it populate the hotels on the map. You can then see where they are located. Look up Rome and then click on Show me on map, put in Hotels and it will populate the map. You can zoom in to the area where the Vatican and the Colosseum are and see hotels in that area. It's a very useful tool.

We have been to Rome twice, and it's a wonderful city. Pick a time of the year when it will maybe be a little less crowded and not too hot.

Keep in mind that historical Rome was laid out prior to cars, buses, etc. ... since you're in good shape, you'll probably be able to walk almost everywhere ... probably 30 minutes max walking from place to place. Surface traffic is a mess. That said, Rome has two major underground subways to move you easily from one side to the other, then you can walk to wherever you're going. Part of the joy of being in Rome is to experience the ambiance of being on the street among the people.

Consider adding the Borghese Gallery to your list of sights. It's a manageable size and has truly amazing art, including some famous sculptures. Entry is via timed ticket, which you should buy direct from the museum well in advance. It's set in a nice park perfect for strolling, especially if it's hot and you need some shade.

The suggestion to get Rick's Rome guidebook (or any other respected guidebook) is an excellent one if this is your first visit. Also take some time to explore the different parts of this site. The At a Glance and Plan pages here are a start: https://www.ricksteves.com/europe/italy/rome. You can use the Search function to find previous threads for hotel recommendations. https://search.ricksteves.com/?button=&date_range=6m&filter=Travel+Forum&query=Rome+hotels&utf8=%E2%9C%93

Booking.com is often recommended to help find hotels, since you can filter for price, location, and amenities. But book with the actual hotel when possible.

I don't want to stay in one end and have to Uber to the other side of the world.

Assuming you are from the USA, the uber you know at home does not exist in Italy.

You use a taxi

When I was in Rome last year, our Uber app from the US worked. They send a taxi, but you pay through the app, which is so much better because you know the price in advance. And you dont have to walk around looking for a taxi stand. We used it a few times. Early morning needing to get to the train station and later one night when we were just too tired to walk another step.

You should prioritize a visit to San Clemente Church-different levels of history uncovered. Also the Pantheon. There really isn't a place that's really central to both Coliseum area and Vatican area.

Have a look at the Albergo del Senato for lodging. On the piazza with the Pantheon, and with the right room, a view of the Pantheon so close you feel like you could touch it.

If you're retired, my biggest tip is to travel in a slow season like November. Rome, is a hot mob scene during the Summer and even the former shoulder seasons on either side of Summer.

I would recommend looking around Campo d’fiori or the Pantheon area. That is our preferred neighborhood in Rome and makes for a fairly easy walk to all of the main sites. It is not super convenient to the train station, but we have used a bus or cab if we need to catch a train. There are multiple cab stands in the area which is an added convenience.

I don't want to stay in one end and have to Uber to the other side of
the world.

Assuming you are from the USA, the uber you know at home does not
exist in Italy.

You use a taxi

A year ago April, for Uber-like performances in Rome, we used the FreeNow app all the time. It ain't free, but it's economical and mostly reliable, and works almost exactly like Uber. I have friends that just returned from Rome, and used FreeNow extensively.

I agree that a good place to stay is the Centro Storico area, Campo de' Fiori down to Trastevere. We've stayed on the Campo piazza three times, and next March we're trying out an AirBnB in Testaccio. First time in Rome, 4 nights is about minimum for an AirBnB stay in my opinion, maybe a little PITA getting set up, but if it's a good one...it's just so much more fun to absorb Roma that way, and probably a better value as well.

Make sure that your hotel has air conditioning. I really like the location of Hotel Smeraldo, but their rooms can feel a bit small. It was fine for me, but if you require a lot of space, it may not be for you. https://www.smeraldoroma.com/en/

I also really like Roman Vacations for day tours. https://www.roman-vacations.com/

Try to book the Vatican Museums either first thing in the morning or late afternoon to avoid the worst of the crowds.

Can anyone recommend a 4 star hotel that would suit our purpose,
having never been to Rome before? I know Rome is huge...

Hi there, welcome to the forum!
1st myth: Rome is huge:
It's not! The historic center, where most 1st-timers will be spending their time, is more compact than you might think. On our first visit (as a couple) we walked everywhere, and mostly everywhere on the 2nd, although we'd ventured further out some days than many visitors do. Public transport is inexpensive and not difficult.

The bullseye for lodgings in the center-of-the-center is near the Pantheon and Piazza Navona. One hotel that comes up frequently on this forum is Hotel Smeraldo; a 3-star property that has seen many recommendations. Understand that the star ratings for hotels in Europe has nothing to do with their quality: it's based on how many amenities they can provide so one that is 4-star with a spa and pool but shabby rooms and less-than-helpful desk staff can rank higher than a 3-star with clean, lovely rooms and friendly desk staff but no pool, spa, etc. Make sense? Give me that 3-star any day! :O). Anyway, if searching for accommodations in center, that's where you might want to look. Booking.com is a good resource for checking out hotels as they provide a location map and verified reviews from travelers who've booked through their site.

We've stayed in the Prati neighborhood and the Quirinale, that last one being easy walking distance from Termini train station. There's no wrong answer unless you really can't -or don't wish to - walk much at all to the top attractions, or are uncomfortable taking public transport...which won't be Uber.

Another vote for Prati. Staying on Piazza Navona and near the Pantheon sounds great because of proximity to restaurants and cafes, but ... remember those restaurants and cafes stay open VERY late, with all the accompanying noise VERY late. My wife and I are also in our 70s, and although we enjoy the exciting ambiance of the tourist area hubs, when it comes time to sleep, we want it to be VERY quiet. :)