I love the idea of helping people, your project idea seems really nice!
I totally agree that you should consider reading in your local nursing home. I visit one in my hometown once a month. Especially the Grannies are so thankful, they appreciate my company a lot. And I don't do a lot, sometimes we're just sitting in the garden talking about flowers or so. Many of them like it when you read to them, so you really should consider doing that. And by the way: To make yourself visible try an own homepage.
Here you can find a com domain for your project. It may help you to find people who can help you bringing your idea to life and also finding people who are looking for someone like you. Many grans are still at home and feel alone, cause family can't find time to read to them, talk to them like they need it. So a homepage seems a good chance that those families can find you.
Good luck to you and your really lovely idea!!