There are facials and there are facials. I wouldn't trust my skin to any of the 'street spas' around because you really don't know what product they're putting on your face and the therapists haven't been well trained. Essentially, if it's a place where you can get foot massages, neck massages, body massages and facials, stick to the massage.
You can try pretty much any of the five star hotels, who all have good spas with professional, well known brands, but they are pricy. I notice the Nude was doing a special offer on Elemis facials at around $880 if I remember rightly which looked good. There are also spas such as Sense of Touch which are good.
Be very very wary of buying packages because some less scrupulous spas will take your money but find a million reasons why you can't have the treatments that you paid for.
As a first stop, I'd recommend going somewhere like the cosmetics counter at Lane Crawford. It sounds as though you might need to change your skincare regimen and you can get advice (and a heavy sales pitch!) from the various brands available for sale there.