My current house, with low-E windows, aluminum siding, and a metal roof? It passionately hates everything about GPS.
But in more-typical (stick-framed, asphalt shingled, vinyl-sided, US-ish) houses? I haven't had any trouble with my very inexpensive u-blox (or perhaps clone) GPS board, a presumed-decent GPS antenna that we were throwing away at work, and dainty little [IIRC] u.FL to SMA adapter to connect the antenna with. (I put this all together just to play with making a GPS-backed, low-stratum NTP server -- which was a much more-rewarding process than it had any right to be.)
It was bizarrely good, in fact: While it certainly saw more birds and presumably had better accuracy when sitting in a window, I had real trouble getting it to cease to operate. It seemed to lock on well-enough to provide time and PPS until I put the antenna into a windowless closet.
That said: The antenna that came with this cheap receiver was trash -- at best, 1/10. It was hard to make it work even outdoors on a clear day. I eventually got sick of looking at that part and binned it.
That gives you another weekend project, and you can reuse your DIY NTP wall clock!
If I am interpreting their request correctly, they want a wall clock that knows where it is -- and also knows what localtime is in that position on the globe.
GPS (plus some hairy lookup tables) can accomplish that.