Is Destiny Still Fun Without PS Plus?

No, not in my opinion. There are still things you can do and accomplish. There are quests and missions that you can still do. But once you get past what you can do, there's nothing really left to do other wait for the next expansion or game update.

When I first got Destiny I had the PS Plus. I'm not the kind of person who plays online with friends all the time. Besides the fact that none of my friends have the game. I enjoyed doing the missions and quests. I like upgrading my equipment and weapons and leveling up my characters. After I had gotten myself stuck with a mission a few times, I'd venture off and play in their crucible. I hadn't played in there before and I was curious to try. 

I sucked so bad at first. I liked playing Control, and I'm sure I had team member who were frustrated with me, but I still had fun with. The more I played in the crucible, the better I became and the faster I got to level up my characters. It was easy to get better gear that way too. So I grew to like playing online much more. 

When my 1 year subscription to the PS Plus was over, I was super frustrated with playing Destiny. I don't have the money right now to get the subscription, but I definitely plan to in the future. Destiny just became really boring for me. There are still a few missions I can do with some of my characters, but I'm stuck on them (Yes, I've looked up walkthroughs for what I'm stuck with, but I'm still stuck regardless. Plus better weapons wouldn't hurt).  With every game update and event that comes around, you need to have PS Plus to do it. Otherwise you'll be left out from the goodies you can unlock with completing some tasks.

So in my opinion, Destiny isn't worth my time without having a PS Plus. Sure I'll still play to kill some time if I have nothing better to do. But other than that, you just can't do much without that subscription once you've done everything you can.