They seem to lean towards minimalistic design, so http://minimalsites.com might help.

They definitely seem to favor a clean, contemporary sans serif aesthetic, so I would look at some typefaces like:

Freight Sans - http://new.myfonts.com/fonts/garagefonts/freight-sans/
Alright Sans - http://new.myfonts.com/fonts/okay-type/alright-sans/
Proxima Nova - http://new.myfonts.com/fonts/marksimonson/proxima-nova/
PF Centro - http://new.myfonts.com/fonts/parachute/pf-centro-sans-pro/
Depot - http://new.myfonts.com/fonts/moretype/depot-new/
Parisine - http://new.myfonts.com/fonts/typofonderie/parisine-plus-std/
Today Sans - http://new.myfonts.com/fonts/ef/today-sans/
Embarcadero - http://new.myfonts.com/fonts/mvbfonts/embarcadero/

IMO architects' taste in typography is anything but contemporary.
They seem to be stuck in the modernist vein, and these examples are conservative like that, traditional modernist identities.

My parents were architects, and used a lot of Clarendon (Letraset) back in the day.
I made a Christmas card, a painting plus words in Letraset Clarendon, c. 1960.
Sorry, Catalonia, that's retro.

Not quite sure what the box kite has to do with Cooper Union.
Yeah, isometric perspective as optical illusion, we get it -- a cliché/meme used in the Harvard logo too, more about the graphic designer's take on architectural design than communicating a business/institution to its audience.

Embarcadero

Excellent font, too bad its license is bloody awful.

Shinn, what about something rooted in tradition like DIN Next or Avenir, or something slabby like PMN Caecilia or Lubalin Graph (which always reminds me of architectural drawings)?

Here's an example I like of an identity for an architecture firm, by the brilliant Kyle Poff: http://www.krop.com/kylepoff/#/set/32698

Kontrapunkt

http://www.kontrapunkt.com/en/about-us/our-own-typeface/

... and it's free.

Forgot to include an image of Kontrapunkt:

http://www.kontrapunkt.com/en/about-us/our-own-typeface/

National by Kris Sowersby is an excellent geometric sans with just enough character to stand out from the herd. IMHO it would be a great choice for an architects identity (8 years ago when I did one for a friend I chose Akzidenz Grotesk, but only because National wasn’t even a wink in Kris’s eye or whatever…)

http://www.klim.co.nz/national_samples.php

For many fonts, logo use is not included in the standard license agreement. There is an additional fee. Read the EULA carefully.

...what about something rooted in tradition like DIN Next or Avenir, or something slabby like PMN Caecilia or Lubalin Graph (which always reminds me of architectural drawings)?

Why does architecture still need to be evoked by referencing the simplest of mechanically drafted shapes, those made with compasses and ruler? How very masonic! Or is it some kind of de Stijl thing? (Architects were not averse to using oval templates and French curves, not to mention quadratic equations to support domes.)

Strange, after such iconic progressive 20th century buildings as the Ronchamps chapel and the Sydney Opera House, and any number of polymorphic Autocaded blobs by Gehry and Foster.

Claire, rather than going on your client's typographic suggestions (WTF do they know? -- didn't they hire a designer to make those decisions!), get your type cues from their work.