Well.. I was lucky. Back in 2004, the SO and I bought a pre-construction house. The builders were local and pretty amenable, so, shortly after all the electrical wiring went in but before the sheet rock went up, my mid-teenaged son and I (with the builder's permission) ran all over the house with Home Depot CAT5E cable, with every room getting two runs, and all the runs ending up in the basement with four-per-cover CAT5E sockets to plug into.
The nice part of that scheme was that RJ11 (telephone) plugs are compatible with RJ45 sockets, so the same Ethernet wiring worked just fine for running telephone cables around.
Given that, at the time, the basement was unfinished, adding another cable to the pile that ran along the ceiling (well, the cross-beams, really) of the basement, through to a crawlspace, and from there into the garage was trivial.
The problem you've got is that you've got no Ethernet cabling from your router to, apparently, anywhere, with the possible exception of your PC and NAS. Which I'm presuming are co-located with your router.
Well, I'd suggest that if you've got an attic (going up) or a basement (going down) available, running a CAT5E cable through the ceiling or floor, respectively, would likely get you closer to what you'd like. The idea being to get that cable into the garage, somehow. CAT5E supports a couple of hundred feet at Gb/s speeds; if you can get the end of that cable near the garage and some power socket, then putting a cheapie range extender into access point mode, on another band than what the Nighthawk is using, is probably the cheapest way out.
Thing is: Mesh networks do their thing, by design, without needing Ethernet cables running between the nodes, and with no slowdown due to the packet collisions that one gets with range extenders. Admittedly, one gets a lot finer control over the wifi with your router (I also own a Nighthawk, much older than yours) and can do nifty things like port passthrough that these "managed" mesh boxes won't touch. Not to mention local VPN support.