I think this problem actually requires two solutions:

1. Users who admit they don't know where to put a question:

I think a 'global' location within the Stack Exchange organization such as:

https://stackoverflow.com/questions/ask

would be a good place to a site recommendation system. It would be an undertaking -- as George Edison notes in the comments -- but I'd be willing to help get it off the ground. Statistically, it would be an interesting classifier problem.

2. Users who think they know where a question belongs:

To address this -- the focus of the OP's question -- I suggest the following considerations:

• Parsing tags may be the most useful meta-data to decide if a question is on topic; however, suggesting that a question be migrated after adding a tag could become quite distracting. If new users are uncertain of how to tag a question, they may start typing simply to see the new awesome tag suggestion popup. Suggesting a site after each tag would become very distracting and negatively affect the user's experience. Hence, if the question belongs on a different site, the migration recommendation should appear after clicking 'Post Your Question'.

• Providing a means to seamlessly migrate a question will lessen the burden placed on the moderators to migrate a question.

• A classifier system won't be perfect. So it shouldn't force the user to migrate a question.

• Education is important, so if this were implemented, I think the users should see the bulleted list of on-topic from the faq for both the current site and the suggested sites so that they can learn where to place the questions in the future.

• Migrated tags won't work, so if the user decides to migrate a question, they should be prompted to retag a question as some sites use one tag naming convention and some sites user another.

So how about a page, much like the CAPTCHA page, which appears after a users clicks 'Post Your Question' and says (Please imagine radio buttons instead of [O]):

After parsing the content of your question, we believe your question might be more appropriate for a different site within the Stack Exchange Network. Please consider migrating it to one of the following:

[O] Super User

[O] Server Fault

However, in our recommendation, we may not be 100% accurate, please feel free to post your question to Stack Overflow (the originally selected site) with the understanding that the community may migrate your question if they feel it would be a better fit and receive a faster/more complete response elsewhere.

[O] Stack Overflow

Please select a site from the list above to post your question.

Then if the user clicks the arrows, they would see expanded descriptions:

After parsing the content of your question, we believe your question might be more appropriate for a different site within the Stack Exchange Network. Please consider migrating it to one of the following:

[O] Super User

is for computer enthusiasts and power users. If you have a question about …

• computer hardware
• computer software

and it is not about …

• videogames or consoles
• websites or web services like Facebook, Twitter, and WordPress electronic devices, media players, cell phones or smart phones, except insofar as they interface with your computer
• a shopping or buying recommendation

Super User FAQ

[O] Server Fault

is for system administrators and desktop support professionals, people who manage or maintain computers in a professional capacity. If your question is about …

• Servers
• Networks
• Desktop PCs that you maintain in the workplace

and it is not about …

• Networking outside the professional workplace
• Running servers at home for personal use
• General personal computer troubleshooting

Server Fault FAQ

However, in our recommendation, we may not be 100% accurate, please feel free to post your question to Stack Overflow (the originally selected site) with the understanding that the community may migrate your question if they feel it would be a better fit and receive a faster/more complete response elsewhere.

[O] Stack Overflow

is for professional and enthusiast programmers, people who write code because they love it. We feel the best Stack Overflow questions have a bit of source code in them, but if your question generally covers …

• a specific programming problem
• a software algorithm
• software tools commonly used by programmers
• matters that are unique to the programming profession

Stack Overflow FAQ

Please select a site from the list above to post your question.

Tags might work ...

Count the number of questions associated with each tag across all three sites, find the tag with highest count, and (if it's on a different site) suggest moving.

I suggested the following for this question How to get new (not algorithm/macro specific) TeX/LaTeX questions to tex.SE rather than SO?

Jeff mentioned that we can make use of tag wiki excerpts. However, I feel that the following message will draw more attention from users who don't notice the tag wiki excerpts.

Here it goes:

1. May be a new attribute (say relatedStackExchange) can be added to tags, not visible to all users (probably just diamond moderators). These attributes will define the website where the tag may be more suitable. For example: latex tag will have the value https://tex.stackexchange.com/ in the new attribute relatedStackExchange.

2. When a user tags a question under latex on Stack Overflow website, the site can check if the tag used on the question has a value in the attribute relatedStackExchange, If it does, then the message shown below can be displayed.

3. If we want to go one step further, the user can click on the box and the question can be transferred to the Ask Question page of the respective site (let's say https://tex.stackexchange.com/ in this case). Also, a new account can be created for the user on the new site (let's say https://tex.stackexchange.com/ in this case), if they don't already have one.

I am not sure how much work is involved in this but I hope this might save time in closing and migrating questions that don't belong on SO but may be relevant on other web sites.

I suggest you edit the tag wiki excerpt to indicate that questions with these particular tags might belong on other sites. These excerpts are now shown at the time of tag entry and offer a way to educate new users about the tag:

Its a nice idea in principle, but in practice its a little too problematic to be useful.

An automated process assumes that all questions are tagged appropriately, migrated appropriately, and that there is a correlation between a given tag set and migration to a given site.

Given the volume of re-tags, and complaints about mis-tagged questions, I'd be wary of using assumption 1 as a major input in an automated process.

I'd need to see some hard numbers on the number of migrations to the number of contested migrations to know if it is worth using as a reliable metric in an automated process.

I'd also need to see some good numbers (maybe the math intern who's name escapes me at the moment) could work on how well tag sets and migrations map together.

I do realize that the suggestion was for a message and not an automated migration - thus there are no irreversible/harmful changes - but I'm just as sensitive to the problem of over-messaging and the problem that suggestion may prompt moves that ought not to be made.

I'd like to hope that brains are engaged, but I've seen too often where otherwise intelligent people do stupid things because "the system said I should" or "It wouldn't suggest it if it was a bad idea".

If sounds like a good idea and it might work nicely.

But, is it worth the implementation effort? And is it worth the extra strain it put on the server to keep track of question/migration history?

I do not know the amount of migrations that happen each day. But if there only a couple per day it just might not be worth the effort/resources.

It would be best to implement a voting mechanism, as it is already implemented for 'delete', 'flag', 'close' a question. Of course this would take into account the users flag weight. It seems to me that this is pretty intuitive solution to a real problem!

A user would suggest a new site for the question, and based on how many similar suggestions, or votes, it would either be automatically moved or a moderator would get the results.

That's the beauty of SE, it's moderated by the community. I don't think it would be fair to undermine the efforts of the users/moderators that lurk here with some artificial suggestion algorithm. Put it in the community's hands, and give them +5 for successful migration suggestions!

There you go! ;)

Too complex.

Most of suggestions like this one are easy to reject because overly complex implementation was proposed for them.

Let's take the most easy and still effective step (pareto principle).

There is still suggestion of simple implementation where 20% effort can solve 80% of cases.

Instead of all-purpose suggestion system we actually badly need to stop the Stack Overflow from drawing energy from its own technology-oriented children and help them to stand on their own legs. The complete list as of Jan 2015: raspberry-pi, drupal, joomla, windows phone, blender, magento, emacs, wordpress, tex. Nothing more.