The monastery complex is small and entirely walkable — you can cover both churches and the terrace in under an hour on foot. There is no transport needed within the site itself.
The surrounding lake shore is a different matter. The beach areas, restaurants, and resort facilities are spread along several kilometres of shoreline, and there is no public transport connecting them. To explore beyond the monastery, hire a car in Yerevan, negotiate with a taxi driver for a few hours, or join a day tour. Walking the shore road is possible in theory but not pleasant in summer heat.