Thanks for the suggestions. The bag I had was fabric-covered, like @kristenabelle described and it held up well for a long time. I'd be content with the same bag, but the brand (Dakota) doesn't seem to be easy to find (I see them listed as made by a company called Tumi, but Tumi's website doesn't seem to list much in the way of Dakota products).
Good to hear your Samsonite luggage lives up to its reputation, @Quattro. Also good to know the four wheels have been helpful. My two-wheeled bag has been pretty stable, but I guess the extra wheels can be helpful.
@NeedaTurkeyLeg, I'd consider the Disney bags, mostly because they'd be easy to spot on a baggage claim carousel, but not sure I could justify the additional expense (and it doesn't sound like they'll hold up as well to air travel). I also like outside pockets and haven't seen Disney bags that offered them.
All good ideas, so far. If anyone else has a favorite travel suitcase and is willing to share, then I'd appreciate it.