The only ethical ways to get closer is to either use a lens with a longer focal length ("more reach"), or to view them in captivity, such as in a zoo.

Trying to get closer to wildlife will only stress them (which you have observed their reaction — to run away).

Without stalking the deer, you can use the approach favored by hunters: be in places they are likely to be before they're there, and wait. Usually that means sitting in wooded and grass/wooded border areas, starting an hour or so before sunrise, and applying lots of patience. Move slowly, stay quiet, and enjoy the time with nature.

Baiting and feeding, even if not directly intentionally "baiting" them (such as your neighbor's bird feeder) is training the wrong behavior into wildlife. While docile animals such as deer don't present much direct danger to humans, the exact same inadvertent feeding behavior also attracts larger animals such as elk, moose, and bears (if they are indigenous to your area). All of those animals can be dangerous to humans, and at best require relocation once they become accustomed to human-provided food sources. At worst, they have to be put down (conservationists use the phrase, "a fed bear is a dead bear").