Bigger tires won't fill the wheel gap, it'll just make the car higher. Also the lower profile you go the more gap you create. I highly recommend you hit up picture loaded threads here and also Google "G35:aftermarket wheels and tires" so you can view a huge variety of choices. It's literally useless to post a "What kind of wheels should I get?" thread because it's such a personal choice. BUT that doesn't stop dozens of new members from doing that exact same thing all the time.
There are hundreds of choices out there so you should find a few you really like, it's a pretty amazing feeling to find just the right set that will completely change the way your car looks and also the way you look at it.
Offset and wheel size are crucial to understand to get just the right combination. Read, read and read some more on threads in this section to get a feel for what will make you happy.
Here's a great place to start: http://panoramic-3d.ru/forums/wheels-...-ask-here.html