I was pleasantly surprised that my local Walgreens (store #07560 in suburban Houston) put in a bike rack upon my suggestion. It took a while, and a few reminders, but it did happen.
Maybe they'd put one in at your local store, too. It nevers hurts to ask.
And if they do it... be sure to thank them for it.
--------- and this follow-up from a fellow Houston cycling activist --------------
Thanks, Peter. Not only does my Walgreen's have a bike rack, they also allow people on bikes to go through the drive-in prescription window.