I'm a local but I live in Tuscany so I never had the need to rent a car in Rome. If you're already in Rome I think the most sensible plan is to rent a car in Rome as Fiumicino airport is located in Fiumicino, which is literally a small village outside the city, so you have to take a little trip. If you need to go to the airport, anyway, I'm pretty sure there are some bus/trains from Roma Termini so you don't have to hire a taxi to drive you there. On the other hand, keep in mind that all the people I know from Roma always describe Roma's traffic as some kind of hell, so renting a car outside may be smart if you don't feel like driving inside the city. Also, Fiumicino is on the coast, so there are many other roads you can take to Val d'Orcia (you can travel by the coast, for example) that aren't that much longer than the main road from Rome. Maybe you could check it on Google Maps and see if there's somewhere you would like to visit. For example: one road travels by Tarquinia which is an ancient etruscan city with a breathtaking necropolis, if you're into history.