Honestly, for most street benches, no—you won’t need any special tools. The typical flat-pack or semi-assembled outdoor bench is designed to go together with basic hand tools you probably already own. A medium Phillips screwdriver, an adjustable wrench or a 10–13 mm socket, and the Allen key included in the hardware pack are usually enough.
If you have a cordless drill, it can speed up driving screws, but use a low torque setting so you don’t strip the wood or the threaded inserts. I’d also keep a rubber mallet and a small level nearby. The mallet helps you tap panels or slats into alignment without leaving marks, and the level stops you from ending up with a bench that rocks on uneven ground.
Some commercial or vandal-resistant street benches are the exception. They may use security screws or tamper-resistant bolts, and those require a matching bit. That bit is almost always included in the package—or you can order it from the manufacturer—so it still doesn’t mean you need a professional toolbox.
A good rule is to read the instructions before you start and leave all bolts finger-tight until the frame is square. Then tighten everything once it is sitting properly. That simple method fixes most wobble issues.
So unless you’re installing a specialty anti-theft model, you can assemble a street bench with ordinary household tools. No trip to the hardware store required.