In late 20th/21st centuries banlieue used without a qualifier refers to what would be called "Inner city" in the US. Faubourg is the neutral one word translation of "suburb" but the word banlieue will mostly be used with a qualifier to endorse a different connotation e.g. une banlieue résidentielle would correspond to a "suburb" in some English speaking countries. If used without a qualifier it can still be understood with its original geographical meaning if context is clear. If someone tells you :

J’habite une belle maison en banlieue.

Then there’s no doubt as to what sort of area they live in. They would not use the phrase if they lived in a ZUP (more or less the equivalent of the US "housing projects").

In a different context when you see newspaper titles such as:

Les jeunes de banlieue, ces « étrangers de l’intérieur assignés à résidence »

Portrait noir de la crise économique en banlieue

we know straight away (and especially when referring to youth) the word banlieue is in this context associated with minorities, poverty, violence, drugs, etc.

There are several ways to translate “suburb” in a more neutral way than banlieue.

In addition to périphérie already suggested by Jylo’s comment, here are two other that come to mind, despite being euphemisms which you rule out in your question:

• autour de
• dans les environs de

e.g.:

Je cherche à louer une maison dans les environs de Lyon.