I am often in homes where the towel bar are placed in odd spots, or they’re too high or too low and look strange. Most on-line sources will tell you 48″ is the right height, but honestly, in most cases, that’s too high.
The correct spot to hang a towel bar is 42″ from the floor. Use that as your baseline and adjust accordingly. I wouldn’t go lower, but sometimes higher works better (for example, in a powder room where space is tight). My personal pet peeve? People who put a towel bar over the toilet. It’s the first thing I remove when I’ve staging a house.
As for where to hang one of those round hand towel holders? That’s simple. Don’t use them. They’re ugly. If you have enough towel bars, you don’t need them. And if you only have room for one towel bar, you can buy double towel bars that are quite beautiful.
Towel bars can be expensive. Check out places like HomeSense if you only need one per bathroom and don’t worry about matching. More than that and you’re best off at a big box store like Home Depot but I’ve found some great stuff online as well.
Toilet paper holders, by the way, can be mounted on the side of bathroom vanities and tucked out of the way. In a small space, like the one at my cottage, rather than mounting one on the wall, I bought a toilet paper stand that I can pull in close to the toilet. It works brilliantly and looks terrific too.