If you have a friend that you've invited over a number of times, but never had that invite reciprocated, you need to find a way to get invited to his house. It may be awkward for you, but you can use some creative methods if you really want to get invited over.
Purchase a plant for their garden. Suggest that the plant needs special attention and you know just how to give it. Make certain that you explain the attention poorly so your friend doesn't understand how to provide it. Say, "I wish I could plant it for you." If she's picked up the hint, she'll invite you over.
Buy a pizza or, better yet, get a two-for-one pizza deal at a place near his house. On the way over, give your friend a call to see if he's eaten yet. If not, volunteer the extra pizza for him. Tell him you'll gladly drop one by since you can't eat two by yourself. Wait for him to invite you over to share.
Hang around with her friends. Wait until you find a weekend where they're doing a project that you can help with. Tell the people that you know all about how to do the project and wait to get invited to their house to help. Study up on the topic if you don't actually know much about it.
Be cool and become the person that everyone wants to have over. You'll not only get invited to that person's house, but you may fill up all the rest of your free time with other people.
Ask him what his plans are for a specific night. Be blunt. Ask if you could beg an invitation from him for that night if it doesn't interfere with his plans.