Pillowfort
Pillowfort.io is a user-friendly space that emerged from people "complaining about the limitations and flaws of these (other) sites, yet lamenting that there was nowhere better to go."
Unfortunately, Pillowfort is in beta and costs a small free to join, but you can try out the platform as a demo user on Pillowfort's website. You may have issues accessing it though — I got an error message when I tried to set up my trial because of the unusually "high amount of traffic" the site is getting.
Dreamwidth
Dreamwidth is a free platform for "creative folk" who want to share artwork and creative writing.
"We'd like to take a moment to reassure all y'all that we have your backs," a post welcoming Tumblr users says. "To the newcomers: we're happy to have you join us. Welcome aboard!"
Mastodon
Mastodon is a decentralized social platform, meaning that its thousands individual communities exist on separate servers, but they all exist under one network. In response to Tumblr, Mastodon created a post with reasons to choose its platform as your new social media site.
"It's a completely decentralised social network which combines the best bits of Twitter and Tumblr, but the technology is structured in a way whereby it can never be shut down," a post advocating the switch to Mastodon says.
For more alternatives, a Tumblr user has created a master list of websites that could be potential options.