Try going to areas where seniors "hang out" ... Church socials, bingo halls, casinos, senior centers, "The Y", etc, etc, etc
Are there any sites for meeting others (seniors) just for friendship. Everything I find is for dating?
I believe you will find it very difficult to find such a site. Most seniors don't bother with a computer to meet friends (they could be like me, totally computer illiterate). Your best bet is to find areas that interest you, join one of them and meet people through them. My wife likes cooking, and learning about other foods, so she joins several sites that specialize in that area (I think one is Sassy Southern Cooking).
Good luck.
Try meetup.com. It organized so you can pick a interest like cooking, book club, or just social. I went on to check what is available where I am and the had several senior groups, or if want an all age roup they have them too.
I have been made friends in an association or a club, today we become the best friends, so the best way to have friendship is , going to join them near your area. Further more, I have a writing friend on internet for a few years as well, we discuss and send emails to each other sometimes.