Yes, urban benches with a backrest high enough to lean your head back for a nap do exist, though they are less common than standard park benches. These are often referred to as "reclining benches," "nap benches," or "ergonomic rest benches," and they are designed with a tall, angled backrest that supports the neck and head, allowing you to recline comfortably.
Most standard urban benches have a backrest that only reaches mid-back level, which is fine for sitting but not for relaxing your head. However, certain municipalities, parks, and private spaces are increasingly installing benches with ladder-style backrests or curved, high-backed designs. Some models even include a slight recline angle (around 10–15 degrees) and a longer seat depth, which helps you shift down slightly and use the upper part of the backrest as a headrest.
For example, in some European cities like Copenhagen and Amsterdam, you'll find sculptural, concrete benches with integrated headrests. In the U.S., urban parks in Portland and San Francisco have installed wooden or metal benches with backs as high as 30–40 inches. Certain "anti-homeless" designs intentionally avoid this, but progressive cities now include inclusive furniture. If you're looking for one, search for "reclining park bench" or "ergonomic public seating" and check university campuses, botanical gardens, or newer transit plazas.
Keep in mind that while some benches offer a decent headrest, they are rarely as comfortable as a bed. A better option for an actual nap might be to carry a small travel pillow. But if you want to lean your head back under an open sky, these niche benches are worth seeking out.