STJ for the day
Can a car handle the Hills of STJ for the day?
Echoing what others have said -- if it's not raining, sure! If it's raining or the roads have not dried out from recent rain, you could be putting yourself in a dangerous situation.
Where are you planning to go? If you only go up to Trunk Bay on the North Shore, or down Centerline to Coral Bay, you'll be fine. All the spots Pia mentioned are very risky without 4WD, as are a couple of spots on the South Shore Road if you make it past Jacob's Ladder.