I'm not in your situation, but I'd expect the answer to vary so much from one site to another that you won't get useful answers, at least not in the way you phrased the question. That is, the Whole Foods you tried might not have worked, but a Whole Foods two towns over (or several states away) might work fine, because of site-specific issues with the WiFi installations. It would also, obviously, vary depending on where you park -- the closer to the WiFi base station, or whatever repeater may be in use, the better; and the fewer obstacles (walls, etc.) between your car and the base station, the better. This suggests that you look for a location with parking very near the building, and you may need to check multiple parking spots to see where the signal strength is best.
Also, Tesla software updates seem to be about 500-600MB (see
this thread, for instance). TeslaFi reports that my car receives an average of one update every two weeks, although there's a lot of variability in that. This suggests the car will be consuming about 500MB to 2.4GB of data in software updates per month. I tried a Web search to figure out what a "typical" cellular data plan provides. Most were either "unlimited*" (with "*" leading to a wall of text, typically saying that if you exceed a limit you'll still get data, but at limited speed) or somewhere between 3GB and 8GB. I have no idea what your plan provides, of course, much less how much data you use. I just checked my own plan, and it's "unlimited*" with a 3GB cap before throttling. I happen to be one day away from the end of my billing period, and so far I've used 237MB of data. Thus, if it were me, and if that 237MB figure is typical, I'd be able to handle four or five Tesla software updates per month over my cell phone without hitting the throttling limit. If your situation is similar, it might work out fine for you, especially if you put off Tesla updates until late in your cell phone's billing cycle. If you try this, be sure to disable the option in the Tesla UI to upload driving data, since that will use more data.