Which heading, if any, should I use for a web app where I divide the content acccording to cities and every city has a page, but I didn't yet write the name of the city on the page?
Is it good just to add <h2>New York</h2> and likewise for every city?
Yes, headings are still relevant for SEO, because they briefly describe topics of sections, they help organize your web page in a clear way, useful to show organized content for end users and help Search Engines to understand your content better.
Designs can vary a lot, so a basic approach to your question would be: If you are listing cities, do they also have a description or do they have some information attached? If yes, put them in headings and the description above. If it is just a list of cities, I don't think it makes sense to put them in headings, but this depends on your design, there is not a single valid answer for such a general question.
I recently read about an SEO experiment where they tried using heading tags (<h1>, <h2>, etc.) and also tried using <div> and <span> that were styled to look like headers (large, bold, prominent text).
Their conclusion was that the tags don't matter. Large bold text that is centered at the top of your content is weighted more heavily by Google regardless of whether header tags are used.
Similarly, using heading tags, but restyling them such that the text is not as big or bold reduces their effectiveness for SEO.
In this day and age there is no reason to use heading tags for SEO. Having prominent, big, bold text at the top of the content helps Google understand what the content is about, but heading tags are only one way of implementing it.
For SEO, are headings still worth it?
Most definitely!
If the page is incomplete, then you probably should not publish it (or at least make it not-indexable to search engines).
In a complete page setup and to get a page advertised on google, its a good idea to have the following:
A wonderful meaningful title under 65 characters. Anything over 65 characters will likely get truncated by search engines when your page is listed in their results. This title goes in your title tag in your HTML (between <title> and </title>)
A short description that is less than 160 characters. In your HTML, the description has the following code format: <meta name="description" content="whatever"> and replace whatever with a description that you expect users to see under your web page title in search engine result pages. I say "expect" instead of "want" because if your description is not good enough, some search engines such as google might take part of your website text and use that as the description instead.
An <h1> tag. The two-character tags that start with H an end in numbers 1 through 6 are header tags and the numbers represent the importance of the text in it. H1 means most important header and H2 means second most important. You can see the importance when you try to use all six header tags together on the screen because the size of the text will be different for each one and of course text in H1 will be naturally the biggest. Make sure you only use ONE H1 tag because that is meant to indicate the topic of the entire page. If you use more than one, then some search engines might be confused as to what the page is about.
Rich quality content users expect to see on your website.
In your situation, because the city names are short, you should expand on it a bit or maybe use longer synonyms of some words too.
For example, if your app is about race cars, you could have one page for new york with the following values for the important fields I described above:
Title: Race cars in state of New York - example.com
Description: See how fast these race cars can go in the new york state in the USA
H1: These Race cars in New York go fast!
As you can see, I used some of the same keywords in each field since I want to rank for them. Here, I'm trying to rank for: Race, Cars, New, York, and Fast. If your paragraphs mention those keywords enough then you will score well with google, but don't overuse them.
No issue, Short headings are relevant for SEO. So, those headings are easily crawled by Google search engine. It is important to keep your heading SEO friendly and easily detected by a Search engine.
