He seems interested but keeps not booking a date: what to do

Look at what he is actually doing. Does he respond quickly and at length, or does he reply in short bursts with long gaps? Does he start conversations himself, or only answer yours? When he says he wants to meet, does he attach any detail, like a place, a day, or a specific thing he'd like to do, or is it always a vague "we should"? A man who is interested and organized will usually propose something specific within a few exchanges. A man who keeps the topic open without ever narrowing it may be enjoying the attention, or may be waiting for you to take the lead. Either way, the absence of concrete plans is information. Notice it instead of explaining it away with his work schedule, which is often true but rarely the whole story.

Your reply has to do three things. First, it should acknowledge what he said without rewarding the vagueness. Responding to his "we should" with another round of banter tells him the vagueness is fine. Second, it should offer something specific: a day range, a type of plan, or a place you'd be happy to go. Specific options are easier to say yes to than open questions. Third, it should leave him a clean way out that still lets him say yes. Something like being fine with a different day, or asking which he prefers, makes a no feel less like a rejection and more like scheduling. Keep the whole reply short. A long message full of enthusiasm reads as anxious, and anxiety pushes people further from committing.

Give him about two to three days before you follow up on a plan he hasn't confirmed, and do the follow-up in the same tone as the first ask, not more intensely. If he replies with a yes and a time, good, move to logistics. If he replies with another vague answer, you have your answer about his follow-through. If he doesn't reply at all, send nothing else for at least a few days. A single message after silence is reasonable. A second unanswered message in a row is not. If the conversation stays dead after that, stop initiating. Don't send the "guess you're busy" or the late-night nudge. Let the thread sit. If he comes back later with a real plan, you can decide then whether it's worth meeting, but you don't owe him a chase in the meantime.