Hi There,
There are some options and things to consider.
1. A wireless G router has about half the range of the newer wireless N routers. Also it's much less expensive. You can position the wireless router behind on near a metal filing cabinet and the range will be diminished. I f you have a laptop you can go outside and actually check if your signal can be "picked up" there.
2. Once you have positioned your router then change the SID name and select the most secure password or pass phrase available for your computers.
3. In your router settings (read the manual or pdf file on the disk) there are provisions for MAC address filtering. On that setup page you can enter the MAC addresses of both of your computers (the MAC addresses of both computers will be listed for you to see so you won't have to hunt for them). Set your MAC address filtering to only allow these two computers to connect.
4. There are network devices that connect ot your house wiring ( just plug it into any 120 volt recptacle in your home ) . These devices do not transmit wirelessly at all. Here is an example: http://www.bhphotovideo.com/c/product/596318-REG/Linksys_PLK300_Powerline_AV_Network_Kit.html
5. Of course the best way is just to connect your router to your computer using Cat5e or Cat 6 cables to the "LAN" ports (ethernet port). That is the most secure method and also the most reliable.
Computers will automatically 'sense' the LAN (or ethernet connection) and allow you to connect.
Running the ethernet cable is really not all that difficult in most cases.
Hope this gives you some ideas,
Al