Running in bare feet is probably the best thing for you, but after humans of spent generations of having their feet, legs, and posture ruined by shoes, you'd need to adjust yourself back into barefoot running.
Running in barefeet forces you, for the most part, to not land on your heels. Heel-strike is the number one factor in running injuries, as all the stress at the heels shoots straight up the legs and to the knees. When you're in runners, all the padding takes away the neuro-feedback that hitting your heels is bad for you, so even though you don't feel it hurting, you're still damaging yourself by running that way.
Furthermore, running in bare feet utilizes an area of your calves that is widely neglected nowadays because of shoes. Bare feet also take away the extra stability that shoes give you and force your leg muscles to fire more and recruit more fibers to stay upright, so it'll be a better workout in general. (This is why a lot of weight trainers will also work out without shoes.)
If you're experiencing pain while running on the beach, it's likely largely due to the sand you're on. Since the ground underneath you is constantly shifting, it takes a lot more of your body's strength to do the same amount of work. You may want to try trail running.
If you're worried about harsh terrain on your bare feet, I also HIGHLY recommend looking into a pair of Vibram Fivefingers. They simulate barefoot running completely and give you no artificial support. The only thing they do is protect the bottoms of your feet from the rough surfaces.