WiFi requires two way communications so regardless of what you do to your router it can't overcome a weak adapter on a device.
Basic steps to increase range and/or speed:
1. Install inSSIDer or a similar application and survey all nearby WiFi APs and look for a channel with the fewest and weakest SSIDs. 1, 6, and 11 are the best channels if they are reasonably unbusy. Determining if a channel is not busy takes a little more effort. It is not problem sharing a channel with nearby users if they are light users. If they stream a lot of video or use their connection heavily it will be a problem for you if you are on the same channel.
2. Locate your router in a central location in your home, higher is better and not inside a cabinet. Adjust the orientation of the router and its antennas and test using inSSIDer to find the optimal setup for your home.
3. 2.4Ghz will have the best range and the best penetrating power. 5Ghz are much more limited.
I have spent time fiddling with the power settings and can't see much of a change up or down.
Without a test chamber as they are now using on this site to run tests it is almost impossible to judge if a change in power made a difference or it is just a normal fluctuation that could be the result of other external factors. When I run inSSIDer and display the signal strength over time it always seems that my signal is fluctuating by at least 5 dBm.
If you want strong signals everywhere the only real solution is to install APs in the area(s) where your signal is weak. Don't bother with this approach if speed is important unless you have the ability to connect the APs using Ethernet cables to your router or at least using Ethernet over power adapters.
Range extenders and wireless bridges should only be used if just having any signal is the only requirement and the WiFi will be lightly used to check e-mails on a tablet or smart phone.
