Just stick to the reputable names, Michelin, Goodyear, BFGoodrich, Cooper etc.

Avoid Bridgestone/Firestone.

Avoid Chinese tires with weird names like Goodride, Everich, and LingLong ...

Buy them from a place that offers good road hazard warranty.

If you have a Costco near you and also membership definitely buy tires from Costco. They sell Michelin, Goodyear, BFGoodrich and have very good prices especially when they are on sale (it's usually like $150 or more off of a set of 4 and free installation). And they stand by the tires very well; I even had a nail go into one tire and even though it wasn't an issue with the tire and not their fault but they replaced it for free.

You didn't specify year, engine, trim level, drivetrain, or any other details but the main thing you want to avoid is Chinese-made tires with names you never heard of. Michelin is generally the safe bet for most vehicles.

Pretty much any reputable brand:

Continental (Germany)

Toyo (Japan)

Dunlop (Ireland)

Falken (Japan)

Hankook (Korea)

GoodYear (USA)

Pirelli (Italy)

And many others…

AVOID sketchy brands, things like Belshina or pretty much all of the Chinese ones…

Although the Chinese are setting up local production of tires, and although they have bough some major tire makers like Kuhmo (popular OEM tire for good handling cars) their quality, from what I’ve been seeing, is still not good at all.

It’s also important to check that you’re buying a reasonably fresh tire.

I would agree with everything above. But although Michelin is pretty dependable across the lineup, a few models are inferior to the competition. 
By the way, you can look at specs on tire rack and see (for each size) where the tire is made. They carry most major brands. 
If you want an all-season tire for a 4Runner, the Michelin Defender LTX is the gold standard. The Continental Terraincontact HT is comparable and a few $ less, though comes in fewer sizes. I’d start with those and go from there. 

I had my tyres replaced with brand new Goodyear F1 Asymetric tyres https://www.tyrereviews.com/Tyre/Goodyear/Eagle-F1-Asymmetric-5.htm The mobile tyre guy told me everyone buys these tyres based on their ratings - economy, handlng and all that, but they just don't last like they used to. Like everything else.

I've had them for about 6 months and done about 3000 miles on them, and they're holding up well. His opinion was that you're better off buying cheaper tyres as the more expensive ones just don't last for years like they used to.

A good set of budget tires from my experience is Kelly Edge A/S or A/T tires. I have their A/Ts on my 4×4 Ranger and I put their Edge A/S tires on my HHR when I was in college, on a budget. The Edges were pretty good. The A/Ts make a bit of tire noise on the highway, but I don't care, it's a truck. They're made in the USA and are bottom rack Goodyear tires.