Generally, the best place to shoot a deer is in the chest. Depending on conditions, it may be difficult to target specific parts of the chest. If the animal is moving, or very far away, or if the wind is blowing, or you are breathing heavily, you may just have to "point" the rifle at the center of the animal's chest, and fire. If you have time to set up a good shot, there are some areas of the chest that are better than others to protect as much meat as possible. Assuming a broadside shot, if you want to hit the deer in the heart, line the vertical crosshair over the front leg (or maybe an inch or two behind it), and line the horizontal crosshair about 1/3 the way up the body. When bow hunting, always aim for the heart if you can. The main goal is that your deer drop as soon as possible. At left, the arrow just barely hit the tip of the heart, opening a gash in a ventricle. A better shot would have been 2" forward and 2" higher.
I try to avoid firing the bullet through the front leg. If the bone or shoulder blade is shattered, you'll wreck the shoulder roast, and generally reduce the scrap that can be used to grind into burger. With a doe or a small buck, you can shoot it in the neck without ruining a lot of meat. Try to keep it very low, close to the chest. If you shoot a large buck in the middle of the neck, you'll loose a lot of meat for grinding. In general, low and forward in the chest is my goal for protecting as much meat as possible. The base of the neck is also very good. This ruins very little meat, and often times drops the animal in it's tracks. The hydraulic pressure wave induced in the jugular vein or carotid artery, renders the animal unconscious, yet it lives long enough to bleed out properly. Try not to shoot the deer in the head. It may die instantly, and will not bleed out as it should. A deer that has thoroughly bled out will taste better. That's what they do in slaughter houses. If you shoot your animal in the guts, you'll create quite a mess. You likely won't ruin all the meat, but it's going to be a serious drag field dressing it. This is especially true if you hit the stomach sack. With great care, you can cleanly gut your deer. Use plenty of clean water to wash out the carcass. Don't age a gut-shot deer. You do not want to give the bacteria a chance to grow and spread. Even with this perfect shot, the deer still ran 125 yards. Needless to say, it bled out very well.