Given Kress, Texas, is a very small town with limited accommodation options, the best area to stay is generally along or very close to US-87, the main highway that runs through it.
This highway corridor is where you'll find the most convenient access to any local services, including the few dining establishments and the town's primary gas stations. Kress is a small agricultural community, and its layout is quite straightforward, with most businesses situated along this central route.
For solo travelers or couples passing through, staying near US-87 offers practicality.