What other content do you want to feed the other rooms? In what format? HDMI? Component? Mixed? Your diagram looks spot on for getting OTA from antenna to the rooms. Do the tv's in those rooms have QAM or ATSC/NTSC tuners? You may be able to use a QAM modulator (do a web search) to inject one or more signals into the stream to go to each tv. As I don't know your budget, I can't tell you if it's cost-effective for you.
The other alternative is to use the cat6 you are running (1 pair, leaving 1 for networking) to setup either a component+audio or HDMI over cat6 matrix distribution system (again, web searches will turn up many options, and there are several threads on here re: same). With HDMI, one drawback is that it works to the lowest common denominator because of EDID requirements - so if you have a TV that is 1280X720, one that is 1366X768, and a third that is 1920X1080, the signal that will be sent to all is 1280X720 (the highest signal accepted by the worst tv in the batch). When I looked at these 6-12 months ago, I don't recall any of them pushing high-def audio signals either, but that may have changed. Again, you haven't spelled out your requirements, so it's just a guess at this point as to what you want to distribute and to where.
Just remember, money makes almost anything possible, so it's a matter of how much you are willing to spend to solve your problem.
The other alternative is to use the cat6 you are running (1 pair, leaving 1 for networking) to setup either a component+audio or HDMI over cat6 matrix distribution system (again, web searches will turn up many options, and there are several threads on here re: same). With HDMI, one drawback is that it works to the lowest common denominator because of EDID requirements - so if you have a TV that is 1280X720, one that is 1366X768, and a third that is 1920X1080, the signal that will be sent to all is 1280X720 (the highest signal accepted by the worst tv in the batch). When I looked at these 6-12 months ago, I don't recall any of them pushing high-def audio signals either, but that may have changed. Again, you haven't spelled out your requirements, so it's just a guess at this point as to what you want to distribute and to where.
Just remember, money makes almost anything possible, so it's a matter of how much you are willing to spend to solve your problem.