I don't know if all cities list that stuff on their library website, but New Orleans' library does. Look for a link for 'genealogy'. You can also call the library before you leave home to find out what genealogy resources they have. Sometimes the genealogy stuff is at one particular branch, so it's good to know which one has the information you'll be looking for.

Will you also be near that state's archives? If so, check their website. Louisiana has an online database where you can look up information on death certificates statewide, and birth & marriages for New Orleans. I write down that information while I'm at home so I know which microfilm to ask for as soon as I get there, that way I'm not wasting valuable time.

Some states, like Missouri, have the actual death certificates online.