Croatia Accommodations

It's a blockbuster year for travel, and I'm particular--I would not do this, but I don't think you'll end up sleeping on the street, just maybe not the nicest spot or location, and perhaps wasting some time. I would at least bookmark things in Booking.com and do some scoping out in advance.
It's been years since my last visit, and May was bustling but not swamped back then, it can only be more popular now. I once had some trouble just showing up in Trogir because a festival was happening that I was unaware of, and it's a small place. I imagine in Split and Dubrovnik you would be okay.
Are you a couple or do you have a kids? That kind of thing would make a difference to me.

It's just us. And, I do realize our choices would be more limited. Just don't want to end up completely shut out.

It's a tough call to be sure--people have gotten so savvy with airbnb and such. You might share you rough itinerary so that more recent travelers can chime in. Some of these villages are really small. If Plitvice is on the agenda, I would book there for example.

We were in Croatia and Slovenia in September of 2019, and it was quite busy and crowded. Weather was still very summery and many people were also on the beaches, not just sightseeing. May is cooler and not beach season so I assume it's not as crowded. However, more and more people are traveling now that countries have opened up and Covid is no longer considered a pandemic. People are just itching to get out and travel again after being cooped up for almost 2 years.

The other thing to consider is how picky you are about location. Would you be happy if you could only find lodging far away? I don't necessarily need luxury but I do like convenient locations. And I don't want to waste time driving around looking for a place.

We are leaving for Scotland the end of May. When I was making hotel reservations last November, I noticed a lot of places were already booked up. I have no idea if Croatia would be the same. Just thought I would mention that.

Will you be driving? If you have a rental car, you will need to find a place either with on-site parking or at least a public parking lot nearby.

Our itinerary currently includes:
Split
Plitvice Lakes
Rovinj
Zagreb
Ljubljana
Lake Bled

We'll be spending at least two days in each place. We will rent a car for Plitvice Lakes and Istria. Beyond that will likely use public transportation.

We are in final plan for our whole trip right now. Into Dubrovnik, out of Ljubljana. Leave in 12 days. Car part of the time. Including many same cities as yours.
Our hotels are almost all booked. Tedious. Have done it both ways on trips before. Ahead of time and on the fly. Either way it takes time. That said we have booked most all before for this trip. All the time it takes now is less we have to figure out as we go. Less contention too. Less time in hotel looking at all the options.
I would say if you want to book on the fly, then don’t look too much now as what you saw might be gone. So if you see a nice place you may want and it is gone later, you have wasted time by previewing. Maybe some disappointment too.
Close transport, close to beach, close to center, all things may be less available or more expensive on the fly.
You will be fine on the fly if you want that. Flexibility is great, in theory. But really what does it get you? Will you suddenly want to stay longer, or go somewhere else? For two weeks you are probably not going to have the time to do that sort of flexing.

You may find things on the fly, but at what cost? What’s available last minute might not be desirable in some way. It could be inconveniently located, not up to whatever your standards are, expensive, or potentially all of those things.

I have done two trips to Croatia and Slovenia without fixed reservations, and it worked out fine. Last was in October 2022. I did ten nights, starting in Split, island hopping for a few days from there, heading up to Zagreb by train, and then on to Ljubljana and home. I booked the first few nights in Split in advance, but otherwise I booked on the fly (using booking.com or AirBnB). I didn't have any trouble.

In May 2015, spent two weeks driving across Croatia and Bosnia and did the same thing. May was not busy that year; the only night I had trouble was in Zadar because of some sort of big event that weekend - and I still lucked into a great place in a prime location booking the night before. Will it be busier in May 2023 due to post-pandemic travel? Maybe. But I think we were hearing the same thing last fall, yet my Croatia-Slovenia trip worked out fine. This kind of travel isn't for everyone, but if you are OK with it, I don't think you'll have much trouble.

Thanks for everyone's point of view. I appreciate all the feedback.