Most middle-aged women (single and looking for a partner) want someone who can be a good friend, an equal, who is sexuality generous and satisfying, and with enough values and interests in common to make it easy to share life.
If you're honest, responsible and easy to communicate with, you're very likely to have a good chance of attracting one.
As for meeting them:
- you could try dating sites like E-Harmony, but take care and learn how to recognise and avoid the fakes.
- I think going to places where people share common interests is a great way to meet; university, adult ed courses, crafts, sports, arts or volunteering in causes that support your values and goals are good examples.
- if you have a friendly dog, dog lovers love to meet and chat while they're out exercising their pets.
Some may be single mothers, and they'll want a man who has zero sexual interest in kids, who can be friendly with them and who'll support her in her methods of parenting.
Some want a man who can provide a home and material comforts. They might also want him to be able to fix plumbing, woodwork and mechanical things. These may be women without a well paid career of their own. Unless that's what you love to do, I'd recommend avoiding these types. They tend to feel 'entitled".