I'll Have to watch those two
Currently Watching Black Clover, and Tower of God (based on a webtoon)
Tower of God, well the thing is in the title a boy and a girl have to reach the top of the tower and fight "God" really interesting since this world is unknown.a good watch also a good read. it's ongoing.
+1 to all of Lobsters suggestions, my fav of that list being Assassination Classroom and Love is War. Lots of good characters and values and lessons you can take from it in AC, S2 is absolutely nuts. Love is War is a great rom-com and is gonna get really good really soon, I've read ahead and it gets to the point where its an easy 10/10 imo. Keep up to date on it, you're not gonna regret watching it rn.
If you ever want to read anything, read Pandora Hearts. Easily my favorite work of fiction ever, across any medium (TV, video games, books, art, anything). The cast of characters are amazing and you will not be able to guess what happens next. I had no idea how the story would change and evolve and its a great read, but I would not recommend it to people getting into anime recently.
My favorite anime is Gurren Lagann, it has its very bad moments where fanservice is just disgustingly in your face or an episode that just looks horrendous, but after the first 10 episodes the story accelerates and the tone shifts entirely. Its a grand adventure and coming of age story. 2007 show that looks better than half the stuff churned out in the 2010s.
I recommend everything else suggested so far but a complete out of left field anime that I recommend to everyone now is scissors seven. It is a Chinese anime that you can watch online or on Netflix. Season two is dropping on Netflix in a few hours so that is what will occupy my time tomorrow.
Gotta recommend Assassination Classroom again, one of my favorite series.
Will edit more than pop into my head but dropped off the anime train to read mangas (definitely have a lot of recommendations if you're ever interested)
Ok I know you said no Dragon Ball Z, but I seriously recommend the Dragon Ball Super: Broly movie but only if you can watch it in high quality! If you watch it on your phone with 480/720p or something, you won't really know what's going on since it's pretty intense. I watched it on an anime website and the animation didn't feel like actual movement, with so much going on everything looked blurry. When I watched it with my lil' bro in theaters it was very different and art lines were smooth. The animation is SS tier level and the higher quality makes a difference.
There's not really any spoilers in it besides mentioning the Tournament of Power once, and I know some people don't like any DBZ because the waits are like a hundred seconds of powering up/sensing the villain/firing ki blasts/etc. but hear me out on this one, this is where it stands out and it has nothing of these complaints. I even bought it since it has some rewatchability, you can watch some clips on youtube to look in a bit. It's an amazing movie, I greatly recommend watching on a monitor/tv if you do watch it, this one's a huge difference.
I've only watched a few and those that I've watched I have enjoyed and those were Attack on Titan, Fairy Tail and Tokyo Ghoul. The first 2 seasons of tokyo ghoul are pretty good but the 3 and 4th are a bit eh.
Based on what you currently have watched, I have a few recommendations. Someone did already steal it, but Hunter x Hunter is one of my top 5 anime. I would recommend the 2011 version. Some other ones include My Hero Academia, Attack on Titan, Akame Ga Kill!, 7 deadly sins and parasyte the maxim. I know its a lot, but they are all anime that I have seen and loved.