There are lots of small villages producing olive oil and one of them, which is also quite famous and characteristic, is Casperia where we suggest to go for a short day trip and taste by yourself. Best month to taste the new olive oil is usually December.
If istead you don't want to loose a day traveling around Rome but you anyway wish to have an idea of our products while in Rome, you can go and visit Eataly (www.eataly.it) where you can find almost everything. You can buy them or taste them or decide to eat overthere. It's a real experience not to loose.