It depends on how you define 'silence', 'smallness' and 'unobstrusiveness'. I have seen a number of people in this forum asking for quiet builds end up with noisy high-power graphics card (I don't think any graphics cards with TDP of 100W or more can ever be absolutely silenced) and a number of HDDs generating airborne engine sound. Everyone seems to have different acoustic acuteness, which in fact may vary with time and can be further developed after his/her possessing a relatively quiet build.
Several options in different form-factors with small footprint cross my mind.
(i) Intel NUC motherboard + Fanless chassis.
(ii) Fanless i3/i5 Laptop (e.g., HP Spectre 13 x2, which is, to the best of my knowledge, the only fanless Haswell i3/i5 laptop) or less-performing (yet sufficient for office work) Bay Trail laptops, most of which are fanless.
(iii) A desktop with smallest footprint akin to "Family" build in my signature.
She uses a computer for web surfing and word processing. I'd love to be able to make something absolutely dead silent for her, or very close to it. Also preferably something small and unobtrusive.