We have these black rolling carts where I work for carrying around litigation documents. I'd imagine something like that would work too, and look less bag lady-ish.
When population density goes up, you are more likely to live close enough to your grocery store to make multiple smaller visits and make quick visits for one-off items you might need. I rarely ever buy more at the grocery store than I can carry on my own and I find the smaller more frequent trips much more convenient than having to plan around one large trip to a more distant location.