A top university.  Just like scientific journals, these organizations sit at the top of a prestige hierarchy that makes them difficult to dislodge, and everyone wants to get into the top schools/journals to show how smart and capable they are.  A university or journal with a strong EA agenda could do a lot to change elite culture, by unilaterally changing the target that everyone else is aiming for.  (Of course, even if EA owned a university like Harvard 0r a journal like Nature, we wouldn't want to completely change the target because that would probably mess things up, as pradyusp mentions in their comment.  Rather we'd just want to nudge things in a marginally more EA direction.  But this could still have huge effects in the long run.)

University of Chicago, and places like the Hoover Institute at Stanford, are perhaps examples of top universities that take a different cultural stand (slightly more conservative / libertarian) compared to the leading Ivy League schools.  I think the existence of U Chicago probably has an outsized role in supporting the prestige of libertarian ideas in elite circles.  (Aka not very prestigious, but imagine how bad it would be without the schools!)  Alternatively, EA could buy a medium-prestige school and convert it more wholeheartedly to embracing wild EA ideas and priorities -- George Mason University is an example of a school with an extremely iconoclastic libertarian department that has an outsized influence on public thought relative to the school's overall prestige.

I think buying a university (more realistically: funding a new EA-themed department within an existing college, like the Hoover Institution or GMU Econ department), or a top scientific journal in a key field, would be more impactful than buying a newspaper like the Washington Post, which is a potential EA "megaproject" I've seen tossed around before on the Forum.  Newspapers are more about mass political power rather than influencing elite & academic opinion.  And the news business is much more competitive -- the likes of WaPo and NYT, although powerful, are less unassailable fortresses of cultural command in today's world than they were in the past.  By contrast, the dominance of top schools and (perhaps to a lesser extent thanks to open-access & sci-hub) top journals, seems to be going strong.

EA is already obsessed (rightfully so I believe) with starting effective-altruism student groups at as many top schools as possible.  Eventually, funding some schools to set up formal academic departments inspired by longtermist moral philosophy, scientific analysis of potential existential risks, EA-aligned economic development economics, or etc, seems like the logical next step.  Just like Blackwell books going through financial trouble, maybe EA could keep an eye out for an opportunity to bail out a financially-distressed but otherwise promising university, and thereby pick up a lot of elite social influence at a bargain price.

MrBeast Youtube channel.

MrBeast regularly spends $10,000-$1,000,000 per YouTube video. He donates money, cars, food, or houses to video participants. In other videos, he plants trees, cleans the ocean from plastic, etc.

Imagine if he donated $20,000 to GiveDirectly, and showed the impact of his donations in rural Africa.

MrBeast is already an incredible altruist. Let's make him effective, too.

An opinion/investigative journalist with great leverage (in their home country). I'm personally from the Netherlands, and would put Arjen Lubach forward. He is well-respected for his critical investigative journalism with a hint of satire. But another figure that would probably qualify (and is more well-known internationally) would be John Oliver from 'Last week tonight'. Such people would be able to get some of the underexposed issues EA is focused on, more in the mainstream. This would potentially drive increase the focus of research and interested investors in this direction. While EA generally does not have a focus on reaching the mainstream. The rather elaborate nature of the aimed investigative journalism makes the information rather high-fidelity. Plus, the presented specific ideas will in this way also reach the people who actually have the capacity to have an impact in a particular area and who would be missed by extremely high-fidelity outreach like books. 

A journal.

Buy a journal. Improve it's processes. Publish higher impact papers using the legitimacy of the previous journal's name. 

The MacArthur Foundation's nuclear granting

It's not clear to me that we should support the MacArthur Foundation's grants on effectiveness grounds alone. But they might be worth it on reputational grounds + effectiveness. There is an entire field of people who will respect EA because it saved their jobs and they are people we want the respect of.

"Since 2015 alone, MacArthur directed 231 grants totaling >$100m in some cases providing more than half the annual funding for individual institutions or programs."
"MacArthur was providing something like 40 to 55 percent of all the funding worldwide of the non-government funding worldwide on nuclear policy”
https://t.co/srsq45ejc7?amp=1 

This isn't my idea.

ht Haydn Belfield for the quoted text.

Blackwell's book store

As Ben Pace suggests, Blackwell's is in trouble and EA could buy it. How much do EA authors spend on marketing over the next 10 years?

Ben estimates buying Blackwell's would cost $15M. How much marketing do you get fro that?

Imagine if you launch Will MacAskill's new book buy buying the book store. I don't think this is a good idea, but I don't think it's totally stupid and I don't know how much marketing spend you get by buying a book store and all the publicity which will surround that?

Cons: It's a current business and it may not be easy to use marketing channels to push on books.

It's a really fun idea, so I am tempted to ignore the badness. This is a problem. This might be a playpumps situation.

 

I think the Christian Science Monitor's popularity and reputation makes Christian Scientists (note: totally different from Scientologists) significantly more respectable than they would be otherwise. 

From Britannica: 

The Christian Science Monitor, American daily online newspaper that is published under the auspices of the Church of Christ, Scientist. Its original print edition was established in 1908 at the urging of Mary Baker Eddy, founder of the church, as a protest against the sensationalism of the popular press. The Monitor became famous for its thoughtful treatment of the news and for the quality of its long-range, comprehensive assessments of political, social, and economic developments. It remains one of the most respected American newspapers. Headquarters are in Boston.

So I would try to buy a dying newspaper, or another media source. Alternatively (and more likely), I would found a new newspaper with a name like "San Francisco Herald" and try to attract a core of editors from a dying media source. 

David Attenborough

Get David Attenborough to give a talk on the beauty and majesty of animals and what we owe to them at an EAG.

EDIT: Just realised you said "only for its reputation", which makes my arguments for Apple less relevant (though it is still a very highly-regarded brand!).

If money is no object, I'd say Apple. It's one of the most loved brands, it is phenomenally good at marketing and it holds enormous financial influence. Not only could you direct a portion of its revenue to EA causes, you could also do things to encourage the spread of EA — for instance, add a "round up" feature to Apple Pay that rounded all your purchases to the nearest dollar, with the money going to EA funds.

Obviously this is not at all possible, but it's an interesting question to think about. Even if no one can "buy" Apple, it's perfectly possible for an EA to eventually become CEO of Apple and that could have much of the same impact.