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I just listened to a podcast where it was said that astronauts have only been at most 400 miles from Earth (except for the moon of course in the '60s/'70s). Is this true?

I know that the ISS orbits at a paltry ~250 miles so lets ignore that!

Have they not visited geostationary orbit at 22-23k miles to maintain or deploy satellites?

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    $\begingroup$ Can you remember what podcast it was? $\endgroup$
    – uhoh
    Dec 30, 2018 at 11:15
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    $\begingroup$ A Joe Rogan show IIRC $\endgroup$
    – Richard
    Dec 30, 2018 at 12:25
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    $\begingroup$ Just FYI, the numbers for that 1970s moon trip: "In April 1970, the crew of NASA's Apollo 13 mission swung around the far side of the moon at an altitude of 158 miles (254 km), putting them 248,655 miles (400,171 km) away from Earth. It's the farthest our species has ever been from our home planet" space.com/11337-human-spaceflight-records-50th-anniversary.html $\endgroup$
    – takintoolong
    Dec 30, 2018 at 13:55
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    $\begingroup$ @takintoolong bingo! Which astronaut travelled farthest from Earth? I'll add that to my answer as well, thanks! $\endgroup$
    – uhoh
    Dec 30, 2018 at 13:59
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    $\begingroup$ No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back. $\endgroup$
    – Uwe
    Dec 30, 2018 at 18:44

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So that's twenty-four individuals that count towards "(except for the moon of course in the '60s/'70s)"

Incidentally, as @ takintoolong just pointed out, the answer to Which astronaut travelled farthest from Earth? is the Apollo 13 crew. According to this answer:

Currently, the crew of Apollo 13 holds the record for highest altitude above earth with 400,171 kilometers (248,655 mi) on 7:21 pm EST, April 14, 1970 (source: Wikipedia). That would be 406,542 km when measured from the center of the earth.

All other known crewed missions have been in "paltry" LEO (low Earth orbit) as you call it.

You'd have to check each space station's maximum altitude to begin to start to look for maximum astronaut altitude excluding Apollo astronauts, but I don't think it could possibly be farther than 500 km or so.

Update: Wikipedia sez:

Highest altitude for manned non-lunar mission

Gemini 11 crew Charles Conrad, Jr. and Richard F. Gordon, Jr. fired their Agena Target Vehicle rocket engine on 14 September 1966, at 40 hours 30 minutes after liftoff and achieved a record apogee altitude of 739.2 nautical miles (1,369.0 km).

Wow!

But nothing even close to MEO or GEO. No reason at all (at least in my opinion and that of lots of others). Instead the focus is on robotic missions to "do stuff" out there in higher orbits. Robots can run for a long time, don't need air or water or bathroom breaks or space suits or sleep... mostly at least.

There was the planned Asteroid Redirect mission that early on had astronauts going into deep space, beyond the Moon, but you can read more about what happened to that in answers to What ever happened to the Asteroid Redirect Mission?.

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Have they not visited geostationary orbit at 22-23k miles to maintain or deploy satellites?

No. It takes a fair amount of energy to get from LEO to GEO. The only spacecraft capable of bringing astronauts plus a satellite to space was the Space Shuttle, and it didn't have enough delta-V to get to GEO. It would deploy its satellite in LEO along with a kick stage, and the kick stage would bring the satellite to GEO.

Between LEO and GEO are the Van Allen belts, which have high radiation levels so you don't want to spend too long there. This limits manned missions to LEO, mostly.

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    $\begingroup$ The Apollo moon flights selected trajectories which skirted the Van Allen Belt(s), to reduce radiation exposure. In effect they flew at the periphery of the belt to the extent feasible. $\endgroup$
    – mongo
    Dec 30, 2018 at 15:15

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