Looks like Uber is available in Rome. May be cheaper.
There are definitely shared shuttle services which used to be about 20 Euros per person.
As for hotels, if you stay in the centro storico, they tend to be boutique hotels or B&Bs. They get nice reviews but they're not like the 5-star hotels.
However, if you're looking to go to all the popular sites on your own, it's nice to be around Piazza Navona or Campo dei Fiori because Corso Vittorio Emmauelle runs east-west, between the Colisseum and Trevi Fountains on the eastern end to the Vatican on the west end of it.
All the public bus lines are there.
Of course you can book tours which have hotel pickups and then it won't matter as much. Hotel tours are good for skipping the lines at the Vatican Museums, Colisseum and some other places. You get a guided tour as well of course.
However, generally, I think the Piazza Navona area is more lively, with restaurants and bars all over, than way up by the Borghese.
For the guided tours, I would look through viator.com and getyourguides.com. If you have smart phones, they have apps. and the tours you book, you can get electronic vouchers that you just show them and you don't have to worry about printing out any vouchers.
Also for something like the Colisseum or the Forum, I'd try to book a day or two in advance or when there's good confident forecast about the weather. Since they're mostly outside, you may not want to be there when it rains. When it's sunny, those places look a lot better but the heat from the sun could be tough, especially in the summer.
Of course if you wait until the last minute to be sure of the weather, those tours could be sold out.
I'd look for the half day or 4-5 hour tours which are often offered twice a day in the high season (march/april to sept/oct). The all-day tours could be tiring and also kind of limit where you could eat and what you could do the first day.
As for what to do on the first day, you can ask the hotel for a local map and they'll show you where the hotel is and what's around nearby. Good to walk around, just kind of walk off the long flight as well as dine. You can ask the hotel for restaurant recommendations or research them on trip advisor and other travel sites.
Google Maps will have tons of reviews too if you happen to be able to get data access on your phones.
From around 5PM on, the restaurants you walk by they will try to get you to sit. I'd avoid those places. The places with the good reviews have no problems getting customers.
. Have points for Marriott.
