Mostly? I end up leaving them unprocessed hidden in some folder on my hard disk, or even in my SD card... for years
OK, occasionally when they do get processed I just keep them on my facebook to share with friends. I've got a photo printer so I've printed the occasional one to show off. Laminated some to use as hand-outs for outreach sessions. Lots of cheap Ikea frames you could use as well.
I have gotten some custom merchandise done (not with astro photos) with my artwork at CafePress. Perhaps that might be an idea? A mug? Bag? Shirts? Lots of printing places that will print anything on anything.