Actually, it is the other way around. Get a very good TV antenna and you will also get very good FM. The FM band is between TV channels 6 and 7, so the TV VHF will work great.
I have a large Winegard TV antenna in my roof/attic crawl space. I patched it into the cable TV junction (which I don't use for cable), and with the help of a antenna preamp to boost the signal, I get TV in every room just by plugging the TV into the cable wall plug.
In the 2 rooms with the audio systems, the tuner is just plugged into the cable wall plug as well. One of those rooms has a small TV, so I just use a splitter.