<p>I have a scenario wherein, for example, I need to repeat a list of US states and display a table of cities and city populations after the name of each state. The design requirement dictates that every outer repetition must be the name of a state followed by a table of cities, and that requirement cannot be changed at this time. Are there disadvantages to nesting a GridView within a Repeater and then binding each repeated GridView during the Repeater's <code>ItemDataBound</code> event? What are some alternative solutions?</p>

If it were me, I'd reverse the question and ask why
I should
use a GridView,  If you need a bunch of built-in features like paging and sorting, then the GridView might be a good fit.  If you just want tabular data, I'd reconsider.  Why?  Because with GridView you're getting a whole bunch of stuff you won't use, your ViewState will be potentially huge, and your page performance will be slower.
I'm not a bigot when it comes to GridView, but I only use them when there is a damn good reason.