Thanks, all - read the search post, used the Google feature, and (to quote Bono) "I still couldn't find what I'm looking for". Maybe it's partially cos next door's TV was still on full volume and after two phone calls and a personal trip to the reception area, it transpired that my neighbour was out but had left the TV on. This HGI has *really* thin walls!!!
And I've found out that the other Hilton Garden Inn in Tallahassee - the one closer to town - has their restaurant open for breakfast service only, but my colleague staying there tells me that it is indeed open for dinner.
I guess you can't trust the websites completely - calling the specific hotel and asking seems to be the only option.