Sounds to me like a very poor attempt at flirtation. You have no need to lie, or fear getting off on the wrong foot. If you are not interested in spending time with this fellow *for whatever reason*, a simple "no" is all that's required. If he confines himself to vague comments about getting a beer "sometime", you can brush that off with "I work a lot. See you around." If he is issuing a specific invitation, you can specifically decline it with "No thank you."
Do not JADE. You do not owe him a reason or an explanation. If you don't have a boyfriend, or specific plans, lying is only going to create drama and draw you further in. Just use polite words and don't engage. If he is pushy, then he is the one being rude. If you must, you can tell him, "I value my neighbors, but I also value my privacy."
If he is fresh out of college, he may just be trying to re-create some dorm-room camaraderie. You are under to obligation to provide it. Hopefully he will be a good neighbor.