This picture here gives you an idea of what they look like.
The Violent Femmes have always struck me as being fairly geeky.
How about The Cramps?
A band whose bio includes the phrase “perverse and glistening sex” can’t be geeky. Geekiness and overt sexuality, in the music world, do not go together. In my opinion.
Ween - ubergeeks. Ubergeeks on drugs.
How about the Minibosses? They do covers of Nintendo songs. And lots of others do the same.
For Geekiest Solo Artist, I nominate Tom Lehrer. Oh yeah.
Optimus Rhyme?
The Arrogant Worms?
MC Frontalot?
I’m not sure if they fall into the geeky category or the nerdy category but how 'bout a little Canadian band called Rush?
They’ve got science fiction stories in their songs like 2112, The Body Electric, Cygnus X-1 (and the sequel Hemispheres).
They’ve got songs about science, such as *Natural Science, High Water * (about evolution), Chemistry, even an homage to the space shuttle program in Countdown.
They’re constantly delving into the realm of sociological science with songs like Turn the Page, Killer Instinct, the Fear series (Witch Hunt, The Enemy Within, The Weapon).
They even get into world history with songs like Bastille Day and Farewell to Kings.
Geeky? Nerdy? A little of both? Have you seen Geddy Lee? 
Geeks in leisure suits - and bowling shirts!
Sloan, especially their breakout hit Underwhelmed
Gotta give it up to Rush as being a trio of geeks.
I’ll add Phish to the discussion. They were all about a few hippie-influenced geeks. They carried on tour-long chess matches with the audience, where there was one move per show. Pretty cool in a geeky sort of way.
I’ll also toss out Yo La Tengo as another candidate. I think their music is pretty mellow & cool, but when I actually saw them? Pretty geeky.
But there is something undeniably cool about their instumental surf-rock version of Blitzkreig Bop.
Speaking of Rush, the song “YYZ” uses the Morse code for “YYZ” (-.-- -.-- --…) for part of the beat. YYZ is the airport code for Toronto int’l.
Brian
One for us old timers
Thomas Dolby
Remember “She blinded me with Science” ?
Bela Fleck and the Flecktones.
Not so much for their personal appearances, but for the music and the audience. The audience at the shows I’ve been to seems to be almost exclusively young white geek types, mostly male.
The music is instrumental, an odd mixture of jazz, bluegrass and world music. Some songs have far out time signatures like 9/8 (“Vix 9”) and 11/16(“Almost 12”).
Bela Fleck is widely considered the best banjo player alive, and the bass player Victor Lemonte Wooten is considered by many to be the best bass player alive. The music is fast, fluid and precise.
Bela Fleck wrote a song called UFO Tofu, which contains musical palindromes where several bars of music are played one way and then played again in reverse. For this song alone, they should be considered geeky.
Throwing Bela Fleck & the Flecktones into the geek discussion without mentioning “Futureman?”
I love that band, and Bela himself is certainly a geek, but IMO, the Wooten bros. are too funky to be considered geeky.
I can do you one better on a geek scale, one tour when i saw them the opener was an electric zyther player named Brian DeWan.
As far as geeky goes, there’s also a Seattle based Harcore group named Bloodhag and every one of their songs i based on Sci Fi authors.
Napoleon of the South
I’m a proud Tennessean…I love that song
The Proclaimers, who would “Walk 500 Miles” and were on their “Way from Misery to Happiness” appear to be geeky too. I wonder if they’re still around.
What about The String Cheese Incident? They sound like they may be geeky too.