Thank you for bringing your question to Just Answer!
It sounds as if this life crisis has been building up for a very long time. It probably would have come to a head sooner if you didn't have the comfort of your high school friend for those seven years.
I know you fear embarrassment, but you may find that your children were already aware of your unhappiness...they often sense it even when it's not talked about. And even if they are upset--this is your life, and you have the right to make the most of the rest of it.
I will tell you that the dating pool is slim for women over 60, but if your unhappiness is great enough that even being alone would be better than continuing the way you are, that should be enough to make your decision on.
There can be great liberation in living alone--not having to answer to anyone else, the freedom to come and go as you like, and enjoying the pleasure of your own company.
Get your finances in order first, because poverty will take a lot of the enjoyment out of your new life. Start getting involved in activities that will give you social interaction when you want it. Explain to the kids that you've been unhappy for a long time, but stuck out the marriage for their sakes...and now it's time for it to be over.
If you have any ambivalence about moving out on your own, consider booking a few sessions with a therapist. Having a neutral party to bounce things off of can be a great way to figure out what you really want. Here's a link to a directory to help you find someone: http://therapists.psychologytoday.com/rms/prof_search.php
I wish you all the best as you consider what the next "act" of your life will look like.