What currently produces your hot water? Is there a mixing valve installed? Do you have lime in your water supply? Are the pipes old and blocked with lime? or rusted inside? Are the pipes undersized?

I'm going to make some assumptions - you tell me if I'm wrong.

Water heater in the basement, possibly at one end of the house. Faucet upstairs at other end of house. Newer house (last 30 years).

For some reason we build houses this way (or with the heater in the garage and the master bath 60 feet of pipe away)

This really sucks if you just want hot water to wash your hands.

An electric point of use heater in series with the regular heater will solve the "just want to wash my hands" issue. It won't supply a shower or bath.

Look at insulating water lines/relocating the water heater to a more central location.

You can add a circ pump and a return line.

A gas tankless located on the second floor near the point of use could be an answer too.

Close the valve at the washing machine and see if that cures it. If not, close the individual hot and cold valves at any sink that uses a single lever faucet, one at a time and test after each time.

Although my suggestion doesn't actually help with your direct problem, something else to consider if you can't find a cost effective solution is to save all that cold water that you may be wasting down the drain before the hot arrives with a 'Cold before Hot' water saver. A simple and very effective device that gives you peace of mind when using any hot tap while waiting for the water to become warm. Good luck.

I would research the hot water on demand thoroughly. Consumer Reports has hundreds of user opinions comments on them and I wish I would have read them beforehand. It takes a long time to get hot water with our gas tankless heaters and I understand even longer with electric. There a greater delay by far than a hot water tank.

I'm going to second WonderDogJake's suggestion of a point of use heater.
My personal choice in the 130+ year old extreme fixer upper I'm living in right now is a circulator, with return line controlled by a timer controlled from the room where the water is used. We actually installed two return lines, one from the end of the long hot water pipe (kitchen sink)and the other halfway through the run (upstairs bathroom). Hitting the timer in the bathroom doesn't cause more pipe to heat up than needed. Check valves are a must on the circ pump to prevent thermosiphon loss of heat up the wrong pipe.
Small 1/25 horsepower 1/2" pumps work fine. They will get hot water 50 feet in about 30 seconds.
An added benefit of the circulator is rinsing dishes if you wash as slowly as I. The rinse water doesn't cool down between uses.
Bell & Gosset has been building circulators for a long time, and all plumbers know them very well if service is needed.

iceqween13- your'e mistaken. How long it takes to get hot water is a function of how much pipe volume there is between the heater and the point of use and how much water is coming out at the point of use. The slight differences between a tank heater and a tankless are going to be based on whether some length of pipe next to the tank stays warm (maybe 5-6 ft) and the second or so that it takes for the tankless to kick on once water starts moving.

That's just basic math. It isn't "greater by far."

If you want hot water faster, you can 1) reduce the pipe size to the point of use (may reduce flow due to friction losses in the pipe); 2) move the heater closer; or 3) recirculate (wastes energy heating a loop of pipe between the heater and point of use instead of a single run).

Thull
Two small polite criticisms of your recirculate diss. Energy wasted with recirculation is less than energy to run a well pump while wasting water to get hot to point of use. Also if your recirculator pumps are user controlled, as in my setup, all of my pipes are heavily insulated, and once hot, will not need further circulating for over an hour.

I suppose that what isn't being mentioned frequently in all of the suggestions is pipe insulation. Its not the prime topic, but always a good idea.