General:
* Peaceful
* Serene
* Tranquil
* Calm
* Still
* Soothing
* Relaxing
* Reflective
* Meditative
* Introspective
More specific:
* Secluded (if it implies a sense of privacy or being away from the hustle and bustle)
* Intimate (if it describes a cozy or close-knit atmosphere)
* Subtle (if it implies a refined or understated quality)
* Discreet (if it suggests a sense of privacy or confidentiality)
The best positive connotation for "quiet" depends on the specific context and what you want to emphasize.