It will really depend where you will be going. Some locations, you really need to rent a car, some others you can take the train, or any type of available public transportation. It will be also depending if you will be exploring the surrounding cities, or just staying local.
Do some online search to see if they drive left or right and see how comfortable are you in driving on a side that you are not used to.
Also take a look how many days you will really be using the car. The days you need just to go somewhere (like from the airport to the hotel, to use the car next day), sometimes the best option is to rent the car close to the hotel you will be staying, and take public transportation or a cab to the hotel. Hotels usually charge you a parking fee and adding it the rental car cost plus insurance, you might be saving some money, just renting the car when you really need it.
I have already booked a car, returned it by the end of the day and booked another one next day... it saved money for parking. Also, depending on the destination you go, many of the economy or compact cars go out of the rental places early, so if you get there a little later for your rental (like at 11am), sometimes you can get very lucky with a free upgrade.
I would also recommend reserving your car rental as soon as your trip is confirmed. After reviewing the dates and logistics, research though the car rental companies and other travel companies, the best prices you can find. Make sure to reserve it and not pay for it. It's worth to pay a little more for not booking at the moment, but that will give you some flexibility in case your travel plans change.
I'd suggest to do also a quick search on bus or train transportations if you want to travel around cities or explore the region. I was able to save at least US$200 during one of my last trips, where we decided to take the bus than driving. We both could relax, not worry about the way there, besides taking tons of pictures and both of us being able to enjoy the scenery. Otherwise the driver can't never enjoy as much as the passenger. Some other destinations, the train is usually the easiest and fastest way around. Not even worth renting a car.
Should I rent a car?
Drive or not to drive.