First off, it would be significantly easier to determine if your neighbor is up to something by looking at the IP assignments on your wireless router. Generally speaking if you go to 192.168.1.1 in a web browser, that tends to bring you to the web interface for your router. Because it varies greatly based on what router you have, I can't really point to exactly step-by-step you need to do. Basically there is somewhere that lists all of the DHCP leasings to specific systems. In that list it will say the host name of the device, the IP address and usually the MAC address. You can see if there are devices there that aren't yours based on the host name (you can check the host name of a computer by going to Computer and then Properties, it should be listed there). Knowing the IP address of your neighbor you can filter your packet captures based on their IP address and port 80 to look at the web traffic. That filter would look like this
ip.addr == <their IP> && tcp.port eq 80
Inside the resulting packets are found URLs and other things that should help you figure out whats happening.
Kind of a side note. Is the reason that your neighbor is using your internet because you have an unsecured wireless router? Securing your wireless is really simple and should be on the top of your priorities if it isn't!