Have you considered carex, tiarrela, huechera and/or hostas, or are you thinking only annuals?

Hi! Thanks for your input! I really was thinking annuals. I haven't heard of carex or tiarrela. I'll have to look them up! There might be too much sun for Hostas. The area gets about two hours of sun at the end of the day around 4-6 Pm. Houston heat with sun is horrible. That's why my impatiens did so poorly last summer. July and August heat and sun did them in.

I'm assuming your 'basic begonias' are the ones grown so often (as you plan to) as annuals, but they aren't really. Used to grow them as windowsill plants in a much cooler climate, and they were basically permanent. Here in so. Louisiana, much the same as Houston, they really are very hard to keep--the humidty, the heat, and as you say too much water gets 'em. I would suggest some cane begonias (often called Angel Wings) which thrive in those conditions and would probably be hardy (or you could dig them up and throw them away, if that's what appeals to you.) Last winter I think I had canes in bloom as well as making pretty foliage, tho' when the winters get a little cold they tend to stop blooming and can even freeze back to the ground, but come back up promptly. Do you really prefer to re-plant every year? There are caladiums that would do well there, including new ones that take sun. Even some ferns prefer some sun and I think look good with begonias. Of course they're not annuals either, nor are the little gingers that would look nice, like kaempferias. Lots more, especially if you don't need to re-do it every year.

Have you considered Sedum varieties? They don't mind hot dry weather and there are so many to choose from. I've got white begonias with a tall sedum growing in the back--they look great together and emerge at the same time in the spring (those are red Salvia between the begonias). I'm not sure what variety of Sedum I have, but it does flower at the end of the summer/early fall with dusty pink clusters---not real impressive, but nice enough.
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