I second the idea of creating targeted areas on the heavy bag. Removable tape (I like painter's tape) is a good option.
You're also talking about basically eye-hand and eye-foot coordination. Dribbling a tennis ball, and progressively smaller balls, can help with the former.
In my experience, muscular control is an overlooked and essential part of kicking accuracy. You need to be able to put your foot where you want it. To this end, standing leg lifts can help. Once you're good at just that bit, try making patters, like a figure-eight, in the air. This sort of muscular control will help you put your kicks where you want them. These are simply supplementary exercises of course.
If you can hang a small target, like a tennis ball, you can try punching and kicking that as it sways. Or, if your'e in an area with a lot of trees, try aiming at the ends of some of the branches with your strikes.
If you have enough space, you can work your coordination a bit while you're watching TV. Every time there's a change of scene, punch or kick towards as specific target- say, the lead actor's left eye. Of course, I'm not advising you to hit your TV. Stand far away enough so that you're not able to touch it. But this sort of exercise will help with target acquisition.
I'm not sure how hitting a stationary makiwara will help you with accuracy.
I third the idea of putting targets on your heavy bag, provided you have proper punching and kicking form. And as Callsign said, another option is hanging a tennis ball from a rope and hitting it as it sways. You can also punch and kick leaves when there's a slight breeze. One more exercise for speed is when you are in the shower and it's dripping when it's turned off, practice by punching as the drip falls. It's good for timing and quickness.
You could take duct tape and make markings on the heavy bag with the duct tape, then attack those targeted areas. That is, granted you already know how to kick and punch properly. I trust you would not attempt to do these things on your own, for even striking a heavy bag can injure you if you do it improperly. Don't hurt your wrists.
Contrary to what some here may say, kata, hojo undo (supplementary exercises) and hitting a bag and/or a makiwara will help you.
Of course without a good qualified instructor to help you learn good form, and control; and going to classes it'll be basically impossible.
Oh and mirrors to watch yourself with will also help. I've also heard people using video cameras to review also.
Be paraniod it is good but if you break someones femur not saying anything.
All I have is a standing heavybag to work with
