moving modum to different place in a room

Perhaps you could switch to another channel on your router.  Of course, you'll have to configure your wireless clients to the same channel.

Reposition the angle of your router.

Place a 2nd wireless router at your proposed location.

I would NOT advice putting in another router like Bruce recommends, introducing another router on your LAN will cause issues with double NATing. You COULD run an ethernet cable and adding another wireless access point (AP) which LOOKS sort of like a router but simply adds another wireless point of connection, you would need to maintain it and secure it separately, not hard but just another piece of equipment you would need to maintain.

I would try the 20' coax cable and moving the modem / router / wireless AP, it is the simplest solution and should cause no issues.  The addition of 20' of coax is typically inconsequential. It's the cheapest route and if it does not work simply move it back and pursue something else.

I'm fairly certain Bruce did not mean another router (forgive me if I'm speaking out of turn) but rather a WiFi Range Extender, which looks like another router but actually takes the existing signal from your base router and retransmits the signal, boosting the effective range and mirroring the security of your base router.  Linksys (Belkin), Netgear, and several other companies make them, they are easy to configure and work very well.  You could also invest in Powerline, a system that extends your network via your existing home wiring.

Bruce does have another good point, use a free WiFi Analyzer app for your phone and go to the various parts of your home to test signal strength as well as the number of networks operating on the various channels.  You may need to change the channel your modem/router is on to a different one that isn't as crowded.  Additionally, if you do decide on a WiFi extender, you can see what rooms have the worst coverage which can help determine where to put the extender.

Good Luck!