I've been twice in Penang, 5 times in Malacca and three times in Kuching and several dozen times in JB.
Weekend trip to JB via Woodlands/CIQ has caveats and they are following:
- If you do not want to spend 1.5h on MY side waiting in immigration line, you need to be at Singapore side before 8AM sharp. Better to be there at 7:30AM.
- Even if you clean Singapore immigration quickly, you might then have 20-60 min wait time for bus and the equal amount inside the bus, usually standing to travel 1.5km in the traffic. That's in addition to wait time at MY immigration
- The same situation is in reverse on Sunday evening. If you do not want to spend 3 hours crossing borders, you need to be at MY side before 3PM. On Saturday evening border crossing times on both sides are OK.
As mentioned before, the obvious place to visit in Malaysia is Malacca. One day is sufficient to see the central part, assuming that you arrive there before noon and leave around 6PM. In this case you will have enough time couple of museums (Peranakan museum is must), walk around city and see historic churches, eat at one of locally recommended places and head back.
Even if you decide to do it on Saturday, it is duable, assuming that you arrive at Woodlands by 7:30 and around 9AM you are at Larkin Bus Terminal (take Grab from CIQ/City Square) to take bus to Malacca. You can hop to the bus from Malacca which takes you directly to Singapore and most likely drops off at Golden Mile complex.
But above plan means that you will spend 3h in each direction on bus, plus 1h-3h crossing border. So in worst case scenario it is 9h spending just to get there and back. You will spend less time going to Changi, flying to Kuching and come back.
However I can suggest you an alternative, which most people have not heard of. Karimun Island. It is not in Malaysia but in Indonesia. There is direct ferry from Harbourfront twice a day in each direction. Earliest departure is around 7AM and you can come back with 5PM return ferry. The trip will cost SGD $60 but will give you a true experience of using time machine and going back 60 years or more. That place is not a touristy destination but again, gives some idea what 'laid-back place' looks like.