Can I use coax outlets for cable modem?
Here's the caveat with old coaxial cable. If this is an older house, it might have cable already, but it's probably RG-59. This is from back in the days of analog signals, well before we were sending digital signals down them. If you have a satellite dish, you'll note they need RG-6 or better. 

What's the difference? Shielding

Now, it's possible there's no interference on those old lines. In which case, stick your modem on and everything should be fine. Your modem should have a web interface and it should tell you the signal strength the modem is getting. Hook a computer to it and then hook the cable up. If you don't get enough signal, you might need to do some work (or call the cable company and have them do it for you, although they might charge you for that).

If you need more signal, here's some tips


Find the main splitter. It might be in the attic, in the basement (if you have one), or is sometimes outside. All your coax will tie into it. With a multi-port setup they probably have a serial splitter. They should have labels saying things like -3.5dB. Your room might be connected to one that says something like -7dB. Make sure it's on one of the smallest dB loss ports. If not, replace it with either another multi-connector (one that has minimal loss) or just get a double-male and connect them together.
Make a new run with better shielding. You should be able to find RG-6 readily, and probably RG-6 quad shield as well. This would eliminate a lot of signal loss back to the cable connection point. You can buy non-compression ends for this as well, if you don't want to invest in a coax end tool.