I didn't realise that were routers available with built-in aerials, apart from the MiFi 3G pocket routers.
It's a pity the aerial is internal, as changing the aerial on a Wi-Fi access point to a higher gain antenna does give a much wider range. In our house, we use to get good coverage up to two rooms apart from the Wi-Fi access point and intermittent (1 to 2 bars) in the kitchen, due to concrete walls. I replaced its 2dBi aerial with a high gain 5dBi aerial and get good coverage throughout the house including 4 bar in the kitchen.
If there is any side to the router that you don't need the Wi-Fi signal going out, you could try placing a flat sheet of tinfoil or even a metal biscuit tin/lid at that side to reflect the signal, such as if the wall behind or to the side of the router is to the outside or garage.
Another good idea would be to make sure there is no obstacle around the router. For example, placing it next to the PC/monitor will cause problems, where as placing it out in the open such as up on a shelf should help give better coverage from it.
Home-made aerial tricks seem to work best for the receiver as you've discovered, as basically you are trying to make it as directional as possible. For example, I have a friend who modified a small metal rubbish bin into a very effective high gain Wi-Fi aerial However, with the Wi-Fi access point, you don't want to make this directional unless you just have the one Wi-Fi client that you are trying to target the signal at.