There are many places to watch browse in SG.
At ion go to level 3 where you would find cortina ( an AD with variety and good for looking ard) and right ard the corner you would find another shop that has more independents watches like mbf, vianney halter ect.
On level 2 there are iwc and patel phillipe boutiques.
On level 1 there are rolex, frank muller, Porsche design, tag heuer, omega and yet to be open panerai boutique.
If you're into watch boxes or pens, there are boutiques on level 4.
On orchard road where ion is located there are a lot of watch shops but primary by 3 ADs, hour glass, sincere watch and cortina.
Just beside ion is takashimaya where you would find hour glass and sincere watches on level 1. There are mont blanc, chopard, Cartier, bulgari on the same level too.
Diagonally across the road, go to a new concept shop by hour glass at Knightsbridge. There you will find luxury stuff as well as watches. If you're into shoes, you'll be able to find Pierre corthay there.
If you're looking at pre loved watches, there are few around orchard and 2 are located opposite ion at lucky plaza on level one, just beside an indonesian restaurant.
If you need more help, feel to ask and the local SG purist would be glad to help.
Cheers
PAt