Same as most who’ve replied here. We aim to be using booking.com or Airbnb or just Google maps to find a hotel/hostel/b&b or whatever anytime from lunchtime onwards. And certainly by about 5pm at the latest, although we are usually flopped out on the bed or in the bar by then. Pre-internet days we called into tourist information offices, used Rough Guides, or just walked in and asked for a room. But….
….You have to be flexible about the sort of place you’ll stay in. Not everywhere is blessed with a huge choice of places to stay. We’ve stayed in some fairly basic hotel & Hostel style places, which have benefit of being cheap but very interesting places to stay with the bonus that sometimes the food is amazing. If you’ve been in Spain and seen those big “Hostals” by the main roads with trucks, workman vans and pickups outside. Those, but they are all over Europe. About €50 DB&B. For two. Extremely clean, but can be noisy (echoey) and not sound proof. Best (worst?) one we stayed (Bulgaria) had hookers in the car park, and sounds of casual sex drifting through the corridors.
You also need a flexible budget as we’ve also ended up in the only room in town that costs way more than you really want pay. Just enjoy the luxury, you’ll remember that longer than you remember the cost.
And, you have to be prepared for you trying find somewhere where there’s a big event on and everywhere is booked for miles around - happened to us this year. We added 100+ miles to a day to travel to an available room in central Spain to get away from a race circuit near Alcaniz (MotoGP was on). Plus as I said before not everywhere is blessed with loads of easily found accommodation. Get ready to do that 100+ miles to start looking somewhere else. The booking sites don’t include all hotels, and in some countries or regions their penetration of the market is very low. In this case and if you aren’t familiar with the language or even the alphabet of the country you are in it can be difficult to find somewhere.
Finally learn to decode booking.com descriptions. Cheapest is rarely best. Room size when taking in helmets, bike jackets panniers or whatever is crucial. 10m2 is tiny, 15m2 about ok, 18+ is what you need. Ask to see the room. They are often the crappiest in the hotel with a view of a wall and above the kitchen vent. Ask to change if you don’t like it. Also make sure food is available at the hotel or reasonably local - look at reviews they give the best idea.
Finally, your trip will be all the better, more flexible and feel far more adventurous for the spontaneity of booking late in the day and not being 100% certain what you’re walking into.