If bags not checked through then the paid luggage storage place is:
- If facing the TPR entrance - on the main shopping concourse to your right and behind you.
- If looking out from the TPR entrance - " to your left and in front of you
not more than a couple of minutes walk away.
It can take up to 20-25 minutes at times to get in to drop off your bags due to queue and similarly to retrieve your bags. When we used it last year to stow our carry-ons during epic 14 hr (I think it was) TPR visit(s) - the drop-off was quick (no q) but pick-up was nearly 25 minutes.
If so desire, and your times fit, then you can book into a free tour to see Singapore which allows you to leave the terminal (and your bags) do the whistlestop tour 2-3hrs door to door and head back to the TPR for a shower etc.
Booking desk is in the opposite direction to the luggage storage and about a 5 minute walk on the same side and in between the transition between gates (shops finish and a long corridor of gates begins right after the almost like a coffee cart booking place.