I am travelling to SG. I will arrive by air and move to JB at night. Any place to store luggage? Thanks!?

1 ) Best place to you is Queen ST . Singapore - JB taxi stand .24 hours.
the taxi stand control office people able to " help " . you need to paid some " small money " some way around S$ 6-8. * is easy for you to travel from there by Bus . services 170 / Sin-JB express / Taxi to JB.
2 ) Tanjong Pager Malaysia KTMB rail station .24 hours .the India guy near wash room able to help. he asking about S$ 6 . * you also can take shower over there . just paid S$ 2.oo *
Not advises for any Value items !
3 ) Mustafa Center 24 hours ! Sergoon Litter India. IS FREE. just put/left you Luggage ( any size ) before the Entry ! the security will give you one card with No for REF ! many tourist do that. !! services is good ! Shopping over there is GREAT too ! open 24 hours. should be another best place to you !
4 ) Very SAFE PLACE ! With Value items .ie Laptop.. ONLY small bag . make use of National Library LOCKED . * 6 / 7 / 8 / 9 FL S$ 3.oo for a day * Library near Queen ST . Bugis Station.
Mon-Sun: 8.00am - 9.00 pm
Closed at 5.00pm on eves of Christmas, New Year and Chinese New Year
Closed on Public Holidays

You could check with the airport personnel upon arrival.

They are very friendly.

I think you might be able to leave your luggage with any hotels but you might have to pay a fee.