The honest answer is that there is no single number, because an urban planter box can mean a small balcony trough, a deep patio box, or a long windowsill container. What matters most is the surface area, the final size of each herb, and how much airflow and root room you are willing to give up. A useful rule is to plan for mature plants, not seedlings, and to leave a little breathing room between them. If you crowd herbs too tightly, they compete for water, nutrients, and light, and they become more prone to mildew and pest problems.
For a typical urban planter box that is about 24 inches long and 12 inches wide, giving you roughly 2 square feet of soil surface, I would realistically fit 3 to 5 small or compact herbs. Good choices include chives, thyme, oregano, dwarf basil, parsley, and cilantro. If you are growing larger, bushier herbs such as full-size basil, sage, or rosemary, plan on 1 to 2 plants in that same box. A 36-inch-long box of similar width can hold about 5 to 7 small herbs, 3 to 4 medium herbs, or 2 larger herbs. A 48-inch-long box can support roughly 7 to 9 small herbs, 4 to 6 medium herbs, or 2 to 3 large herbs, provided the box is deep enough and the plants have similar sun and water needs.
Spacing is the most practical guide. Give small herbs about 4 to 6 inches between plants, medium herbs about 8 to 10 inches, and large herbs 12 to 18 inches. Also check soil depth: leafy herbs such as cilantro, parsley, and basil usually manage in 6 to 8 inches of soil, while rosemary, sage, and thyme do better with 10 to 12 inches. Group herbs with similar water needs together, and keep aggressive spreaders such as mint in their own pot or a separate section of the planter. If you are sowing seeds directly, you can scatter more seeds at first, but thin them to these final spacing guidelines. In short, a realistic urban planter box usually holds a small, carefully chosen collection rather than a crowded herb meadow: often 3 to 5 herbs in a compact box, 5 to 7 in a medium box, and up to 8 or 9 only when using small, well-behaved varieties.