To go there, you can take a bus from either Jurong East, Kranji, or Woodlands MRT. I usually take SBS170 from Kranji. The price is around $1 per ride. Expect some congestion in Malaysia immigration if you go on weekends, especially on daytime.
Before going, be sure to see the alighting point. Buses from Singapore can alight in one of two terminals: Kotaraya or Larkin. I prefer Kotaraya since it’s closer to Singapore and have more attractions (in fact, I’ve never alight at Larkin).
Meal is inexpensive compared to Singapore. Usually they have the same nominals but halved currency! Last time I ate for lunch for only RM 5, or $2.5, for a fried rice plus orange juice. Even if you shop you get cheaper prices (I saved $5 when buying an Anlene milk!). The two shopping malls worth to visit are City Square (high-end) and Plaza Kotaraya (low-to-med, but has a supermarket).
If you seek nature, you can go to the nearby public park to the west of immigration checkpoint. Inside you can also visit the zoo, Sultan’s palace, mosque, etc. The beach is located even more west at Danga Bay. I visited there but only during the afternoon. Good to try during the night as it is famous for the nightlife. To watch movie you may try the Cathay Cinema in City Square. The price is around RM 10 for a movie.