Jae,
Here is another consideration:
Say you stay in Rome for a few days, you can train it (from Termini) to Orvieto. The schedules meet most travelers' plans.
It is about one hour from Rome. You can take the funicular uptown. In the Piazza, you'll come face to face with the gorgeous, active Duomo - https://en.wikipedia.org/wiki/Orvieto_Cathedral
Orvieto is a quaint, "hill town" of sorts. It is in the Umbria region. Very walkable, traveler friendly, inexpensive, beautiful scenery. You may not be able to visit vineyards as stated in your OP, but, here is an alternative:
https://www.orvietoviva.com/en/orvieto-wineries/ Orvieto is well known for its "Classico" wines.
Florence is a two-hour (fast train ride) from Roma Termini. Get off at Santa Maria Novella (SMN.) Important to know the names and stops. The train may "read" a different end point, but as long as SMN is part of your ticket, you're okay.
It is always a very good idea to read each attraction's, site's, Church's policies - Italy is very strict with some things.
If you are fortunate to secure "timed entry tickets" for an attraction, make sure you are there 15 minutes ahead. If you happen to be just a few minutes late, they may not, more on the "not," won't allow you in. There have been reports from some who were unfortunate to lose track of time for whatever reason and were not allowed in.
Read up on how to get Euro, how to secure your extra Euro and cards. Don't put anything of great value in a pocket or bag pocket where it can be easily accessed from someone behind you. That includes your phone. Don't lay your phone on a table, don't hang your bag on the back of a chair.
Rome is relatively safe. But don't give peeps temptation. Don't make yourself a target or vulnerable. Think "big city awareness." Inside Termini Station is where you should be aware of your surroundings. There are police there, but they can't catch everyone.
All in all, Rome is terrific! A lot of friendly, helpful people < use caution if someone random comes up to help you with your ATM (Bancomat) withdrawal or buying a ticket from a kiosk at the train station. Either go to the window clerk or look for the official ticket associates.
If you happen to take a bus in Rome, (you probably won't, lol unless you take Express #40 to The Vatican), make sure you validate your ticket right away in the machine located in the bus. Transit Inspectors randomly stop buses in the city, board, inspect passengers tickets. If you don't have one to show, you could or would be fined a lot of Euro.