Here' s my choice newer record shops located in Singapore.
All of these have well curated stock, and knowledgable staff. Being fairly downtown, you can combine visiting these with great food, and sight seeing.
Here's my selection -
Curated Records in Tiong Bharu
/ curatedrecords
Hear Records in Chinatown / hearrecordschinatown
House of Turntables in Millenia Walk
/ houseofturntables
Analogue Vault and Analogue Room in Esplanade
theanalogvault.com/
Let me know which are your favourite shops, and I'll look at adding them into Part 2