Yes. Just grab a commuter bus on the highway. Any of the hotel staff may be able to orient you on how to do this. When you get to La Romana call up a telephone taxi (about RD$50) to take you to Altos de Chavon.
You may also consider renting a car for a day to go to Altos de Chavon, visit Bayahibe and spend the day at one of the eastern beaches, such as Dominicus public beach. Get together with another couple to reduce costs for the day. Just make sure you get back by daylight, because the road is still under construction and can be tricky.