Is there a defined/standard way to determine the relative cost of staying in a particular city?

There cannot be a correct way to determine the relative cost of living, simply because each person has a different “basket” of needs. If you like it cool and damp, your HVAC costs are going to be a lot higher in Scottsdale than Seattle; if you like it hot and dry, it will be the other way around.

But you did not ask for the correct way; you asked for a standard way, and there I can help you.

In 1986, The Economist magazine invented “the Big Mac index” as an informal measure of purchasing-power parity. The index is the local price of a McDonalds Big Mac in the local currency, translated into US dollars at the going rate, divided by the price of a Big Mac in the US. So, in 2008

1. the average price of a Big Mac in the US was $3.57
2. the average price of a Big Mac in the UK was £2.29
3. So the exchange rate should have been $3.57/£2.29 = 1.56
4. the actual exchange rate was $2.00 to £1
5. since (2.00-1.56)/1.56 = 0.28, the pound was overvalued against the dollar by 28%

Basically, you could say that life in Blighty was 28% more expensive than life here in Eagleland.

The Economist did this mostly as a joke, but it must have filled a need, because economists embraced it enthusiastically. It is simply, intuitive, stable, and easy to calculate. You can go here for the current Big Mac index for countries all over the world. (I notice they list India, at a scary -70%, even though they don’t serve Big Macs in India. I don’t know what that means.)

Is the Big Mac index applicable for your specific need, short-term stay? I think it is. A Big Mac is exactly the kind of thing that travelers will consider buying. Give it a shot. You can even calculate it for your own city versus the destination city, just by making two phone calls.

You could try https://nomadlist.com/ which compares;

The best places to live and work remotely for digital nomads, based on cost of living, internet speed, weather and other metrics. For startups that work remotely and digital nomads.

Initially built for, and by, nomads (professionals who can work remotely it can show cost of living for locals, expats and nomads (stays from 3 months upwards), and you can sort by cost of living for each type of stay. Not sure how they calculate this information but I believe its crowdsourced.

It includes other information such as connectivity and safety. Overall quite handy and probably closest to what you’re looking for.

Another promising option is numbeo.com, also crowdsourced, but which seems more flexible in calculating costs of living in function of your personal style. The cost of living estimator is pretty neat.

In my office, we try to evaluate these costs when we send people overseas to make sure that the incomes are comparable. We do not want that people are worse off because of high rental costs or higher tax burden.

After working on this for many years, the conclusion is that this is extremely difficult and complicated for people who stay longer in a country, and even more so for people who stay only a short time.

Why?

If you stay for a long time, people can be expected to live a lifestyle that is comparable to the local population. They know where to get cheap(er) food, they do not need to get a haircut in the hotel and they can live a bit further from the city center. If you are new in a town, you foremost care about convenience since you most likely will not have a car etc.

Much more important however, once you live longer in a foreign city, you (hopefully) learn to live within the local circumstances and not the ones you know from home. A 500 sqm house with 2 SUVs and a consumption of 1kg of prime beef per family is something that works in the USA but not in Japan.

The result is that the most you can usually do is to calculate large expenses that are influenced by outside factors such as for housing, tax or schooling. Once you are a tourist however, what you spend money on is so highly diverse per person. Are you willing to take public transport or do you prefer taxis? In some cities taxis are extremely cheap, in others very expensive, and this does not even correlate with the other costs in the area.

For longer cost of living one has to know the target city well, know the tax laws and many other factors to make a good estimate. Otherwise it is likely that you are 20-30% off your estimate just because you overlooked that in country A you need to pay a huge deposit on a apartment rental and in country B you do not need to do that.

For short trips the best one can do is compare things like room costs in international hotel chains, VAT, exchange rates, availability of public transport and then combine items like the Big Mac index and others to try to estimate your expenses.

Another thing that has to be added is that articles that are published in newspapers about “the most expensive place to live” are highly misleading if you do not know the exact things that give a country a high or low rating compared to other countries. For example, some countries might be high because housing is expensive. If housing is provided through other means (company apartment, hotel corporate rates etc), some of the most expensive cities might slide down easily 5 to 10 ranks in the list. Same goes for other rankings such as safety btw. In many cities the safety ranking is affected by traffic accidents and not by crime for example and people taking the subway will not be affected by those.