An aristocratic Heian woman did not move very often. She would not have played sports, nor would she have spent time on long solitary walks. Instead, wealthy women lived extremely sedentary lives, spending much of their time sitting around, playing board games with others, practicing penmanship, or eagerly anticipating a response to a sent poem. This is yet another reason why Heian women dominated Japanese literature of the period to such a degree – there was nothing else to do but sit and write.
To modernize this behavior, spend your time sitting around your room. Talk to your friends on the phone or online. Start writing in a notebook or a blog. Or just feel melancholy. The choice is yours!
But whatever you do, don’t go for a jog. It’s really not very Heian.