Pintrest
If you need a more direct Instagram replacement to keep doing the pictures in squares thing in a public space you can curate, pintrest is an option. It's still social media but I feel like it's less soul suckig. More for the vibes. (from Jai's post about making a personal pintrest)
Send more photos in the groupchat or to your friends
If it's really just the sharing photos with those you love thing. Share them with the specific people you want to see them! Be shameless, maybe you'll start a thing! Maybe you'll all share photos in the groupchat, a great way to stay in touch.
Digital albums and physical scrapbook
This has been my favorite but the most removed way of replacing Instagram. I like digital albums because I can add in my one photo a day or have my favorite photos of myself and be vain and have it be just for me to look through. And I like scrapbook because they help me flip through the past vibes of the time. Which are usually the two things I want from insta. And scrapbooks have the bonus of letting me include other little memerobilia, drawings, notes.
In no way is this a comprehensive list, but you just got to find very specifically what aspect you are itching to keep and find the best way to actually be doing that. But the pull of Instagram attention is definitely there. As someone who used to post regularly I get it. But once you bite the bullet, you don't actually miss it as much as you think you will.