Start by figuring out what kind of metal and finish you have. Most urban outdoor furniture is powder-coated steel, aluminum, or sometimes stainless steel. That matters because stainless steel can often be polished, while painted or powder-coated steel needs a touch-up paint repair if the scratch goes through to bare metal.
Clean the scratch first. Wash with mild soap and water, then wipe with isopropyl alcohol or a wax-and-grease remover. If there is rust, remove it with a small wire brush or rust remover and treat the spot with a rust converter or zinc-rich primer. Do not sand aggressively unless you have to.
For light surface scratches or scuffs, try a metal polish or an automotive scratch remover on a microfiber cloth. Rub with the grain, not against it. On brushed stainless, follow the original grain direction with a non-scratch pad and then polish. This alone can make many scratches disappear without any paint.
For scratches that have cut through the color coat, use a color-matched touch-up paint. Automotive touch-up pens, enamel model paint, or powder-coat touch-up paint can work. Shake it well, apply thin coats with a small artist's brush or the pen tip, and only fill the scratch. Let it dry between coats. If the scratch is deep, apply a little metal primer first, then the color. A thin clear coat over the top will help match gloss and protect the repair. If you do not have clear coat, a tiny bit of clear nail polish can seal a small edge temporarily.
Once the paint is dry, blend it. Use a fine polishing compound on a soft cloth and lightly buff the edges. Do not over-polish, especially on textured powder coat. Finish with a coat of car wax or a non-yellowing outdoor sealant to reduce future rust and make the repair less noticeable.
You do not need to repaint the whole piece unless the damage is widespread or the coating is failing everywhere. Spot repair is usually enough for city benches, bollards, patio chairs, and tables. Just work in the shade, keep the repair small, and match the sheen as closely as possible.