Piriápolis is a more laid back version of Punta del Este with fewer fancy restaurants and clubs. Having said that it is probably more convenient for couples and elder people.
The tourist office next to the Casino or inside the bus station offers maps, tours and general information.
Piriápolis is about 100 km/65 miles east of Montevideo. From the terminal “Tres Cruces” buses depart about every hour during the day, specially in the high season (December to March). Try to get a direct one, they are a little more expensive but you’ll get there in less than two hours. If you travel to Piriápolis directly from Motevideo’s airport, it is about 80 km/50 miles but not all the buses that depart Montevideo “Tres Cruces” station stop by the airport so you need to plan accordingly. If you are staying in Punta del Este, then Piriápolis is about 55 km/35 miles west and bus service is also good. Having the hotel arrange a day trip from Punta del Este to Piriápolis is an option. Costs of these day tours would be about triple what the bus ticket costs by itself but still very reasonable.