Lots of photo hosting options.
I've use photobucket and imageshack for years.
Sadly all are blocked by my office, so I can't see images hosted at those sites.
Makes eBay at lunch annoying as many listing link to outside image hosting.
Then there's the dead/broken link problem, where the hosting site deletes safer a while, it the user deletes to make room for new stuff.
BTW, the album link doesn't work with Tapatalk. I just get the BBcode.
I used imageshack for a long time until they started wanting money to upload images. Imgur is far superior in functionality and it's free. And, you are correct, albums do not show up on Tapatalk. I generally avoid using albums in my ECF posts for this very reason. Albums work great for reddit however.