Generating a random alphanumeric string of length N
Taxi, 2577 bytes
Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 1 l 1 l 1 r.[a]Go to Heisenberg's:n 1 r 1 r 3 r.Pickup a passenger going to Cyclone.Go to Go More:n 1 l 3 l 3 l.Go to Starchild Numerology:e 2 r.62 is waiting at Starchild Numerology.Pickup a passenger going to Cyclone.Go to Cyclone:e 1 l 2 r.Pickup a passenger going to What's The Difference.Pickup a passenger going to Divide and Conquer.Pickup a passenger going to Divide and Conquer.Go to Divide and Conquer:n 2 r 2 r 1 r.Pickup a passenger going to Trunkers.Go to Trunkers:e 1 r 3 r 1 l.Pickup a passenger going to Multiplication Station.Go to Cyclone:w 2 r.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to What's The Difference.Go to What's The Difference:n 2 l 1 r 3 l.Pickup a passenger going to Addition Alley.Go to Starchild Numerology:e 1 r 3 l 2 r.1 is waiting at Starchild Numerology.63 is waiting at Starchild Numerology.Pickup a passenger going to Addition Alley.Pickup a passenger going to The Underground.Go to Addition Alley:e 1 l 2 r 3 r 1 r.Pickup a passenger going to Joyless Park.Go to Writer's Depot:n 1 l 1 l.ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789- is waiting at Writer's Depot.Pickup a passenger going to Chop Suey.Go to Joyless Park:n 3 r 2 r 2 l.Go to Chop Suey:w 1 r 1 r 1 l.[b]Pickup a passenger going to Narrow Path Park.Go to Narrow Path Park:n 1 l 1 r 1 l.Go to The Underground:e 1 r.Switch to plan "c" if no one is waiting.Pickup a passenger going to The Underground.Go to Fueler Up:s.Go to Chop Suey:n 3 r 1 l.Switch to plan "b".[c]Go to Joyless Park:n 1 r.Pickup a passenger going to The Underground.Go to Narrow Path Park:w 1 r 3 l.[d]Pickup a passenger going to KonKat's.Go to KonKat's:e 1 r.Pickup a passenger going to KonKat's.Go to The Underground:s.Switch to plan "e" if no one is waiting.Pickup a passenger going to The Underground.Go to Fueler Up:s.Go to Narrow Path Park:n 4 l.Switch to plan "d".[e]Go to KonKat's:n.Pickup a passenger going to Riverview Bridge.Go to Riverview Bridge:n 1 l.Go to Narrow Path Park:e 1 l 1 r.Pickup a passenger going to Post Office.Go to Post Office:e 1 r 4 r 1 l.Go to Sunny Skies Park:s 1 r 1 l 1 r.Pickup a passenger going to The Underground.Go to The Underground:n 1 r 1 r 2 r.Switch to plan "f" if no one is waiting.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 3 l 2 l 1 l.Switch to plan "a".[f]
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Taxi is super not made for this but you can do it! I'll try to explain what's happening below the un-golfed version.
Go to Post Office: west 1st left 1st right 1st left.
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery: south 1st left 1st right.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park: north 1st left 1st left 1st right.
[a]
Go to Heisenberg's: north 1st right 1st right 3rd right.
Pickup a passenger going to Cyclone.
Go to Go More: north 1st left 3rd left 3rd left.
Go to Starchild Numerology: east 2nd right.
62 is waiting at Starchild Numerology.
Pickup a passenger going to Cyclone.
Go to Cyclone: east 1st left 2nd right.
Pickup a passenger going to What's The Difference.
Pickup a passenger going to Divide and Conquer.
Pickup a passenger going to Divide and Conquer.
Go to Divide and Conquer: north 2nd right 2nd right 1st right.
Pickup a passenger going to Trunkers.
Go to Trunkers: east 1st right 3rd right 1st left.
Pickup a passenger going to Multiplication Station.
Go to Cyclone: west 2nd right.
Pickup a passenger going to Multiplication Station.
Go to Multiplication Station: south 1st left 2nd right 4th left.
Pickup a passenger going to What's The Difference.
Go to What's The Difference: north 2nd left 1st right 3rd left.
Pickup a passenger going to Addition Alley.
Go to Starchild Numerology: east 1st right 3rd left 2nd right.
1 is waiting at Starchild Numerology.
63 is waiting at Starchild Numerology.
Pickup a passenger going to Addition Alley.
Pickup a passenger going to The Underground.
Go to Addition Alley: east 1st left 2nd right 3rd right 1st right.
Pickup a passenger going to Joyless Park.
Go to Writer's Depot: north 1st left 1st left.
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789- is waiting at Writer's Depot.
Pickup a passenger going to Chop Suey.
Go to Joyless Park: north 3rd right 2nd right 2nd left.
Go to Chop Suey: west 1st right 1st right 1st left.
[b]
Pickup a passenger going to Narrow Path Park.
Go to Narrow Path Park: north 1st left 1st right 1st left.
Go to The Underground: east 1st right.
Switch to plan "c" if no one is waiting.
Pickup a passenger going to The Underground.
Go to Fueler Up: south.
Go to Chop Suey: north 3rd right 1st left.
Switch to plan "b".
[c]
Go to Joyless Park: north 1st right.
Pickup a passenger going to The Underground.
Go to Narrow Path Park: west 1st right 3rd left.
[d]
Pickup a passenger going to KonKat's.
Go to KonKat's: east 1st right.
Pickup a passenger going to KonKat's.
Go to The Underground: south.
Switch to plan "e" if no one is waiting.
Pickup a passenger going to The Underground.
Go to Fueler Up: south.
Go to Narrow Path Park: north 4th left.
Switch to plan "d".
[e]
Go to KonKat's: north.
Pickup a passenger going to Riverview Bridge.
Go to Riverview Bridge: north 1st left.
Go to Narrow Path Park: east 1st left 1st right.
Pickup a passenger going to Post Office.
Go to Post Office: east 1st right 4th right 1st left.
Go to Sunny Skies Park: south 1st right 1st left 1st right.
Pickup a passenger going to The Underground.
Go to The Underground: north 1st right 1st right 2nd right.
Switch to plan "f" if no one is waiting.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park: north 3rd left 2nd left 1st left.
Switch to plan "a".
[f]
Start: Get stdin
Pick up the stdin value as text, convert it to a number, and go stick it somewhere to wait.
Plan A Part 1: Get a random integer 1-62
Get a random integer and then get 62 as a number. Duplicate both the random integer and the 62 because we'll need them later. You can only carry 3 passengers at once so we end up with rand, rand, and 62. (The other 62 will wait around until we get back.) Go divide rand by 62 and truncate the result to get an integer. Go back to get the other copy of 62 and multiply it by the truncated integer from the division. Finally, subtract the product from the first copy of rand. This gives us a number 0-61. Now we have to go back to pickup a 1 and add it to the result to get a number 1-62. Yes, all those many lines of text are just mod(rand(),62)+1.
Plan A Part 2: Create an array of characters from which to choose
Pickup a string with all the valid characters and also one at the end we don't want (more on that later). The 63 we picked up earlier matches this string length. Take it over to Chop Suey to have it broken into individual passengers.
Plan B: Move the array so we can select a character
One by one, move every character over to Narrow Path Park. It's the only stack available and the only way to not have leftover passengers getting in the way. Everything else in Townsburg is FIFO so I would have to go back and clear out all the passengers every iteration of the overall loop. This way, I can just leave them at the park and they'll get pushed out of the way by the 63 new characters every time. The very first A is likely to never escape.
Plan C: Prepare to select a character
This is really just a few stops that didn't need to be in Plan D. Re-position the taxi in preparation.
Plan D: Get all the characters we dont want
Starting with the first character in the reversed "array" (this is the 63rd character we don't want), keep picking up and concatenating characters as we count down from the result of the mod function in Plan A. Once you hit zero, the next character is the one you want.
Plan E: Drown the ones you don't want and return the chosen one.
"[P]assengers dropped off at Riverview Bridge seem to always fall over the side and into the river..." Well, that gets rid of that concatenated string of losers. Go pick up the next character and send it to stdout. Finally, let's check how many characters we've printed thus far. Back to Sunny Skies to pick up the stdin value we left so long ago. Subtract one and, if the result is more than zero, send it back to wait and start over again at Plan A.
C (gcc), 57 55 52 bytes
Thanks to 2501 for the pointers...
i;f(n){for(;n-=isalnum(i=rand()%150)&&putchar(i););}
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Jelly, 5 bytes
Missed a trick - see ais523's 4 byter
ØBX$€
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How?
ØBX$€ - Main link: n
€ - for each in range(n):
$ - last two links as a monad:
ØB - "base digits" - yields list of chars "01..9AB...Zab...z"
X - random choice