What are some solutions for tight hamstrings, quads, and Achilles tendon?

Eccentric exercises. The best solution for tight hamstrings and Achilles are stretching and eccentric exercises. Eccentric exercises load and strengthen muscle as a muscle lengthens versus when it shortens. For the hamstring my favorite is the nordic exercise. For the Achilles my favorite is reverse toe raises (heel drops) on an elevated surface such as a stair or step.
Strtching. A physical therapy/ flexibility program is probably the best. Pilates is good also. You can start with "googling" the various stretching excercises for those muscles.

Related Questions

There is pain in my right leg above my ankle and just a little to the left of my Achilles tendon. What could be causing this pain?

A few things. It could be achilles tendinitis, a bursitis, a never irritation or something else. Seeing a podiatrist or orthopedist should help provide a more specific diagnosis.
Neuritis. It may have injured it and it is now swollen putting pressure on the sural nerve.

How far does the Achilles tendon ascend in the leg? What is a common diagnostic tool to diagnose injury/disease of the tendon that isn't ruptured?

1/3 up the leg. Achilles tendon merges into your gastro-soleus muscles about 1/3 up the leg from the heel. MRI is the best diagnostic tool to see inflammatory changes or tears. Real time Ultrasound examination shows full thickness tears.

Are there any tendons in back of the leg below the knee besides the Achilles tendon?

Yes. The plantaris tendon and posterior tibialos tendon both arise from posterior muscles of the leg and connect to the foot. The Achilles' tendon is the largest of the posterior tendons.

When place my finger on my achilles tendon and move my finger up my leg I can feel a vertical split. Is this normal?

Yes. The tendon is attached to the heel by a very thick ligament that kind of fans around the heel an that is what u feel. Google the image of the tendon.

I have pain in my Achilles tendon when I start running on the treadmill only. On the left leg mostly. What should I do?

Slow down. Slow down and rest. Do not go back to exercise until pain is gone. When you go back to exercise, make sure that you stretch well. You could end up rupturing your Achilles. That is a big deal required surgery.

I am experiencing heel and back of ankle pain. On the Achilles' tendon area, higher up in the leg, there is an indention and then a knot above it.

Achilles Rupture. As a sports medicine physician/Trainer I bring some expertise to answering this question. Additionally, I suffer from chronic Achilles tendinitis and once sustained a partial rupture running to catch a bus! This may be a partial rupture of the Achilles tendon or it may be tender nodularity of the calf muscles due to myofasciitis. A rupture limits mobility and ROM of the ankle join. Come see me!