Coax is just about the cleanest cable there is. (At least, good coax is.) The problem is splitting it, since it's an analog signal and can't be simply re-broadcast. Every time one wire turns into more wires, the signal strength and your signal to noise ratio go down.

So, you don't need to worry about length of a coax run. Mostly just number of splitters between demarc and modem. (And shitty connectors... Crimp, not twist-on.) If you have one long run of coax that already goes close to your network closet, put the modem there and use a splitter with a 2ghz bandwidth and low decibel drop. If it splits into three wires, use a splitter with three outputs. Don't leave empty connections. The best arrangement is to split the coax once, and have that one split go to all of the destinations. An ideal 1-to-5 splitter will have a higher attenuation than a 1-to-2 splitter, but if you combine a 1-to-2 with a 1-to-4 to get 5 outputs, the 4 coming off the second splitter will be much weaker than the one coming off the 1-to-2.

You'll want the modem to be accessible so you can easily reboot it if needed, and they do generate heat so inside an air conditioned area is best. If in a box, make sure it has ventilation so warm air can rise out and let cool air in.

What ends up being the best arrangement depends on the geometry of your home. You'll have no problems whatsoever getting Cat6 from your modem to your network closet, no matter where the modem is. But you will need to access the modem every now and then, and like /u/dcoulson mentioned having them all on a UPS together is nice. Personally, I would optimize the coax layout to have the minimum possible number of consecutive splitters (going for one big split, instead) and choose the modem location based on that. (This probably means not putting the modem right at the demarc, since best case scenario that automatically cuts the signal strength of the rest of your house's coax by half.)