I have a week in Italy would like to fly into Rome perhaps spend a day, and then rent a car, could I drive the Amalfi Coast, how long would it take, on a budget, where would I rent a car. Need some help and advise on how to get the most out if Italy in a week on a budget. thank you all so much

Thats all a little vague cyndee.

What is your budget?
You can rent cars anywhere.
You can do the Amalfi coast in a week, sure, but it's not known as a budget destination, nor is Rome.

With one week. Choose 2 places.

Possibly...
Fly into Rome
Rome ...3 days
Train to Amalfi... 3 days
Fly out of Naples.

a...I GUESS YOU ARE RIGHT VAGUE..OK WHAT WOULD YOU DO IF YOU HAVE A FREE FLIGHT TO EUROPE...BUDGET ABOUT 1500-2000...STAY IN ONE PLACE OR RENT A CAR...THANKS

I think you could spend a week in Rome or Amalfi Coast...you dont need a car for either.

If you are alone, then a rental car consumes alot of the budget (unnecessarily). Rental cars make the most economic sense with two or more people. The Amalfi Coast road has a reputation as being 'curvy and hectic' anyway.

Use public transporation. Do Rome and at least two nights on the Amalfi coast.

What time of year? In what currency is that 1500-2000 budget? Are you willing to stay in truly budget lodging? Would you consider an area less pricey than the Amalfi Coast?

I'd drop the car idea, especially as a solo traveller. When you're both the navigator and the driver, you miss a lot. Additional costs (fuel, tolls, parking, maps) eat into a tight budget.