In the evening...
The boardwalk stretches along the shore facing the South China Sea. The best time to go is during the evening, when you'll meet lots of families taking a walk after dinner.
Areas around Mersing have very low light pollution, which is perfect for studying the heavens. Since Mersing is near the Equator, you have a clear view of both the Northern and Southern hemispheres, and thus be able see the Big Dipper and the Southern Cross at the same time. The Milky Way is especially beautiful to view here.
Places like Teluk Godek, Teluk Sari and Tanjung Resang are within half an hour's drive from Mersing, and are excellent observation points for astronomy buffs. You can enjoy dinner in Mersing, stock up on necessities and then enjoy a whole night of stargazing.
Fishing by the jetty
From early evening to late night, people come in droves to fish at the jetty. You could watch them, or you could also join them!