Searching for Good Headphones & Headphone Amp

I currently use an Audio Refinement integrated amp coupled with Tyler Acoustics Linbrook Monitors. However, as my PhD-aspirant fiancée (in the middle of her dissertation) more often than not needs total quiet in our small apartment (save for when we share listening sessions!), surprisingly I find myself in need of good headphones under $100 (new only) and an headphone amplifier.

For headphone amps, I’ve read good things about Channel Islands at 6moons, but have never bought anything from CI. I don’t need anything overly ambitious, and I don’t want to spend a disproportionate amount on the amp compared to the price of the ‘phones. However, I do need these sooner rather than later, lest I be too long without listening!