Exercise Choices for Bad Tendons in Feet

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I have a hard time finding exercise that I can do because of painful tendons in the soles of my feet. They are incredibly weak to the point that attempting to balance on one foot for 30 seconds with the help of a barre, for instance, leaves me with foot pain for hours.

I have Wii Fit Plus and I love the games, but anything that requires leaning such as skiing, balance games, or even the bicycle cause pain that keeps me from working out for at least a day.(Leaning in one specific direction such as during ski jumping is the worst.)

I have bought new shoes with good support and new cushioned supportive socks. They help a bit, but not nearly enough. I have no access to a pool. My doctor says there is no way to strengthen the tendons. I try to do a lot of arm movement to add some intensity. I don't own a bicycle. Would thus be a good option?

Any suggestions out there?