I had the same issue when I replaced my vanity. There wasn't any good wall space to hand a hang a towel ring/holder so we place our hand towel folded over the front of the sink.

What about a rack that goes over the top edge of the door, put it on the inside of the door.

https://www.containerstore.com/s/bath/racks-hooks/12

I would not hesitate to mount a rack.holder to the cabinet. Console/washstand type bathroom sinks often have a towel bar intreated in the front.

How many do you need to hang?

I hesitate to mount on the cabinet because of the cabinet finish.
I see lots of real estate where it looks like in the kitchen especially they have hung towels over the front of the sink and it has affected the finish on that cabinet.

Plus then people drip on the floor. I went back and forth about this and hung one on the wall to the left side of the vanity, overhanging the vanity top. The towels will rest on tile.

Another option might be one of those Command hooks that come in various finishes. I've seen the ones with a brushed nickel finish used in a bathroom for hand towels. They matched the finish on the other bathroom hardware.

Similar to these...if you happen to have a small spot on the wall or the side of a cabinet.

I have no issues hanging towels on the wall behind and next to the toilet. It's the perfect spot. Most bathrooms won't accommodate anything else. It's the norm. A good friend of mine has the racks for cabinet doors you want so I know they are out there. Good luck!!

I use a command hook on the door side of the sink to hang my hand towel....it is just a plain white command hook but matches the tile.

I have a very small bathroom ..so I hang mine on the back of the door next to the sink

I use the pretty paper ones (disposable) in the guest bathroom. I put them in a tray on the countertop. I find that guests are hesitant to "use" the fancy cloth ones.

And WHY is it that builders never consider the placement of towel rods when "designing" a bath????

chiflipper, I was going to mention the disposable guest towels. I've occasionally used them in our guest bathroom. Bed, Bath and Beyond has all kinds of trays/containers for them and a nice selection of the disposable towels.

Do you have room for shelves above the toilet?

We have the same issue and we keep a towel rack attached to the door.

Inspiration: This mini rack could sit on the toilet.

Southbeach Collection Vanity Top 2 Arm Guest Towel Holder · More Info

Hartley Court · More Info

My Houzz: Meaghan and Trevor: Welland, ON · More Info

Sharp Residence · More Info

I too use the disposable paper ( decorative ones ) placed in a wire basket holder, more hygienic, but I’m a bit of a germaphobe ....

Our master bathroom is far down the line for a redo. A hook works great for the hand towel and makes it a little more likely that Husband/kids will hang it up if it falls or put out a fresh one.

Powder room has a small ring next to the sink. Master bath towel bar is next to the vanity on the wall, but I usually keep a hand towel on the vanity top.

Thanks for all the ideas. I will definitely be using some of them in one of the bathrooms I'm redoing. I had a brainstorm yesterday where I install an appliance door pull as a small hand towel rack on the front of an open shelf on my vanity. It won't be resting against a wood door, and it will be next to the sink. At least that's my idea for now.

I had small wall space near my master vanity sink. I had my contractor cut down a regular towel bar (so it matched my actual towel bars) and installed it near the sink.

Basket of wash cloths. Get a new one each time to dry my hands.

I have no problem with a towel bar above the toilet, it's better than the ones under the window next to the toilet. My kids' towels, hand and bath, hang on bars on the back of the door.

In my kitchen I have a long drawer pull on the cabinet door under the kitchen sink. It works great and hasn't damage the surface.