To give you an idea of the size of this city, I live about 35 miles north of downtown, and I'm still in the greater metropolitan area. My son lives in the SE end, a full hour from here when traffic is unimpeded. There is city all along the route, also. You DH may have as much as an hour's drive from the international airport on the NE side to the west side of the city - actually maybe more, and that's if traffic is flowing.
If you Google the address of his hotel or the place of business where he'll be, there is an option under Google Maps to "search nearby". You could then try terms such as "quilt" or "fabric" and may be able to figure out what would be most convenient. Then people who live near those locations can give more precise information. "West" could mean just west of downtown, or it could mean what is commonly known as "the Galleria area" or it could even mean "Katy", a town to the west of Houston, that like my neighborhood is probably included in the greater Houston area. There are many miles between those locations. I'm sorry I don't have a better idea of what to suggest.
I hope your DH has a safe and enjoyable stay here. It's the best time of the year to visit, before the weather gets hot. The azaleas are starting to bloom, and it's quite a show!