Good question! While I agree that traditional metrics (bounce rate, time on site, etc.) may not be directly useful, the same metrics may be more meaningful when seen at a more micro level.
A 56% bounce-rate or average time of 142 seconds per visit at website level may not tell you much about the content/user-engagement, but add some additional layers like traffic-source and landing page, and this will become very useful.
This should be clearer with three distinct cases below:
- Restaurant-hotel specific page: If the user lands on a hotel/restaurant specific page through a Google search (Very often, you'll find Yelp pages of restaurant listed higher than that of the restaurant itself) and leaves without clicking on any other page, you may not have much to worry about. You may actually congratulate yourself for good SEO: User was perhaps looking for just the hotel address or phone number for a specific hotel and yours was the first page in search results.
- Internal search results page: If the user lands on your search results page through a Google search (Example: A Google search for "indian restaurants in Berkeley" may lead to a Yelp search page for "indian restaurants in Berkeley"), you may be more worried than in previous case, but still things are not that bad. Perhaps, your search algorithm is not producing relevant results, or may be the layout of the search page needs restructuring.
- Paid search/external campaign landing page: Finally, if the user lands on your page through a paid search and leaves without converting (no matter how you define conversion), you are losing money on each such user. For this case, a high bounce rate may be a very bad news!
- Conversion: For any website, this is one of the biggest engagement metric. The definition of conversion would vary from website to website and industry to industry. In the case of the mentioned websites, some possible conversion metrics would include: Booking hotels, reserving a table at a restaurant and claiming daily-deals (like Yelp offers).
- Number of Reviews/Number of unique reviewers: Since these websites are almost wholly about user-generated content, these are two very important metrics. While the former metric is a measure of content-generation, the latter is a good measure of website's most highly engaged users, i,e, the writers.
- Frequency of visits: If the frequency of visits for a user (Tracked via login or cookies) is fairly high, there may be no cause of concern, even if the average time per visit is low. This is especially true for websites like Yelp and TripAdvisor. Taking a personal example: Even as a Yelp addict, my visits to the website/iPhone app are fairly short: very often less than a minute! But the number of these visits more than make up for the short duration.
- Internal search usage: More often than not, visitors on these websites are not looking for a specific hotel/restaurant. They are looking for a type of restaurant/hotel in a specific location. (4* hotel in New Orleans or Ethiopian food in San Francisco, CA). If I am Yelp, I would be more concerned about the frequency of usage of the search functionality and the rate of click-through of the search results, and relatively less about the time that they spent on individual pages. Of course, I would like to see some conversion, but at least, I know the users are sufficiently engaged.
- "Upvotes", "Follows" and other interactions between users: Most of these websites have a built-in up-voting mechanism ("Mark as helpful", "Like", Vote as "Cool"/"Funny") that allow users to Vote up quality content. Similarly, many of these websites allow users to follow each other or add them as a "friend" or leave other users a compliment. While at the individual level, this is useful to identify quality content and power-users, at the website level number of such interactions can also be considered a great metric for user-engagement!
- Check-ins: Most of these websites (at least I know about urban spoon and Yelp) allow users to "check-in" at hotels/restaurants. If your users remember to check-in on your website at a restaurant in the middle of a party/date, it's good news for you: they are highly engaged!
- Social media sharing: Finally, a good measure of quality content and user-engagement these days for any website is the content shared on popular social networks. This indicates that the content is not only good enough to be read, but also interesting enough to be shared with friends.
See question on Quora