In most cases all of the Cat5/Cat6/RG6 is ran to a single location, which may be in your basement in the mechanical room. I would suggest staying away from any extenders unless you don't have the infrastructure in place to create a more reliable solution. If you have (RJ45) ports in convenient locations around the house, and they all run to the homerun location where your telephone modules and whatnot might be, get the modem/router set up down there so you can feed any locations that you need to get network from. I'm going to make a safe bet that your incoming line is NOT going straight to the 3rd floor because that would be silly. They probably spliced it up there because that is what you chose as a convenient location for your home office needs.
If you manage to move it to the home location, connect the Cat5/Cat6 cables for the locations where you think you might need wireless, and go out and buy a hardwired AP to install into those ports.
I would personally suggest Ubiquity, but it takes some effort to get everything set up.
Ubiquiti Networks - UniFi(R) AP They have all kinds of models, if you want something good make sure you go with their UAP-PRO or UAP-AC model, which is an 802.11ac AP.
With this you have an affordable, fully managed solution, and it isn't going to force you into a new mortgage like with any cisco product.
EVERYBODY goes out and buys a range extender without taking any time to consider what their options are... NO, do NOT do that lol.
Digerati's already given you a lot of good advice. I don't really have anything specific to add other than a quick run down of a few of the techniques I pulled in my own home to resolve our WiFi signal strength problems (we also have thick internal walls and previously had very poor signal strength pretty much everywhere when we had only a single WiFi router in the centre of the house.
Range extenders are great - but if you have old routers lying around (our ISP used to send us a new one every year or so for no apparent reason so I had various working spares) you can reconfigure those old routers into additional access points. If your primary router is on 192.168.0.1 you would configure the second router's IP to be 192.168.0.2, would disable DHCP on the second router, and would set the primary router's DHCP range to start at 192.168.0.3 (and further up for more routers). Some also have a "Range Extend/Access Point" mode you can enable at the flick of a button to sort this all out for you automatically. You may also like to set all of your WiFi networks to the same SSIDs (differing/automatically found channels usually works best though) and passwords for convenience of access.
You then have a question of how to get internet to those second routers. Some with those "Range Extend" buttons work great as... range extenders. Some don't though, and sometimes because they're not purpose built range extenders can't boost a weak WiFi signal (also needs to be strong enough in the first place to get a reliable connection).
I personally use Ethernet Powerline adapters (
Google - I personally use the TP Link AV500 most of the time but have a hunt around for others too) and have nothing but positive things to say about them. I've used a number of types in different houses and have found them to work incredible reliably even across large houses and different ring mains. Some also offer WiFi outputs.
In my house I have the primary router near to my master phone socket, which connects via ethernet to a few computers in that room, then via ethernet to a powerline adapter which goes to a few other rooms (other computer in study, internet connected TV, etc.) - which are all again connected via ethernet to those powerline adapters. Some of these also connect to routers which provide a WiFi signal or are WiFi enabled powerline adapters for my various mobile devices.
From where I used to be with a patchy WiFi signal in the centre of the house I now have a really strong WiFi signal across the entire house and reliable ethernet internet for all my fixed devices. Works flawlessly for me and only cost me the price of the powerline adapters as I had two spare routers lying around and the powerline adapters came with all the ethernet cables I needed.
Richard
In addition to setting all of the SSID's and passwords, it's important to also set the channel width to the same for every AP in order for zero-handoff to work properly, and AFAIK it is not possible to connect automatically between 2 radios on different frequencies (2.4Ghz vs. 5Ghz for instance).
For safety and expansion, I would also avoid setting the DHCP range that low. Typically I use 100-199 for the last octet on a /24 network.
As a final note, range extenders should not be confused with access points. There's a huge misconception about these two terms. I would probably never use multiple range extenders in any case as it would be a nightmare. If you have routers that you configure as AP's the best thing to do if possible, would be to use them as network switches to get them internet from the feed. Just connect it to one of the LAN ports (not the WAN port) and you're good to go.
@OP - based on the description of your problem, I can nearly guarantee that you have a port on that 3rd floor in the bedroom where your modem/router is currently located, because I have never seen the incoming feed ran to anywhere but the basement. So you would have an AP up there hardwired, and probably move the router to the basement for some wireless down there. Hook up the router to any other hardwired locations and install more AP's in locations that lack WiFi.
NOTE: I am only assuming that your box is a modem and router in one. This seems to be the trend for all newer modems. Otherwise you'll have 2 boxes, probably one with a coax line being fed to it (modem), and the router, which is connected to the modem over a category cable (Cat5e/Cat6 most likely).
