I believe for most Singaporean JB is quite common.
Here is simple tips for first timer.
I know there's many ways to get into JB but these are my preference.
SBS 170 from Kranji MRT Station.
(For higher chance for SEATS do not crossover)
SMRT 950 from Woodlands Interchange
Once you complete the Malaysia Immigration, you can choose to walk to CITY SQUARE or take the Singapore Public Transport to Larkin (Malaysia Bus Interchange/Market) or Kotaraya (Bus Interchange)
I have stayed at Putri Pacific Hotel (quite near the City Square)
Citrus Hotel (opposite City Square)
both I like... however Citrus Hotel is just like a budget hotel...unlike puteri pacific ya...
I hope this help if you decide to stay over at JB, here are two hotel that you might consider.
check the hotel websites for more details...