What is an area close to cities that has a higher number of people, or population density, than a rural area

That would be a suburb. Outside of most cities are smaller residences or suburbs. It's not as hectic as the big city, and most will have access to public transportation and apartments(suburbs closer to rural areas will most likely have neighborhoods), but a more relaxed atmosphere, similar to a rural area. I hope I helped with your question. Have a good day!

suburban

Explanation:

taking the usatestprep activity rn