Tough to say. Taxi's are all over the place, but it adds up depending upon where you are going. I doubt you eclipse 90 bucks a day (typical island rental). I woud suggest that one day you do rent a car and hit the NE section and go have lunch at Vies or head to the SE section and go to Salt Pond and hike out to the Rams Head in the latter part of the afternoon.
BTW, hitch hiking is quite popular. I picked up a couple of people when I was driving. So don't be afraid to ask for a ride.