When searching for a person's burial (in whatever place or country), there are often a couple of "routes" you may have to try out to find this information.
A good place to start (as you have already done) is looking for a gravestone on various sites like Find-A-Grave. Also take a look at more local websites like the Iowa Gravestone Photo Project and IAGenWeb Project (Johnson County). But keep in mind that coverage on these sites is far from perfect. Many cemeteries are only partially indexed. Some gravestone have been destroyed. Some are still there but illegible. Some people – probably most people – never had a gravestone erected to their memory. So there are numerous reasons why this can be an unreliable way to find where someone is buried. Note that even if you find a gravestone you cannot be certain a person was actually buried there; their name may just have been added to the family gravestone.
If you cannot find a gravestone on one of the popular grave websites (which is often the case), you need to look for cemetery records. These can vary greatly in availability and content. Many cemeteries kept burial registers of some sort, as well as deed records to keep track of who owned which burial plots. Once you have found a paper-trail in cemetery record you can go back on the hunt for a gravestone, because then you should know which cemetery and hopefully have a plot number to make locating the gravestone much quicker.
For locating cemetery records it really becomes a game of probabilities. I am assuming you don't have any clues from a death certificate or obituary that suggests where she was buried. What was your grandmother's religion? This can play a major role in determining where someone is buried. Take a look at a map and do a quick Google to locate the nearest large cemeteries to where your grandmother lived or died. Make a list of the most probable places your grandmother might be buried, remembering that sometimes people were not buried where they died and often were buried with or near to other family members (parents, spouse, children, etc).
Knowing nothing else about your grandmother's circumstances, my first place to search for someone who lived in Iowa City would be Oakland Cemetery. Luckily, this cemetery has an excellent online database and map that you can fully search by burial and owner.
If your grandmother was Catholic then a starting cemetery to search would be St Joseph's Cemetery. If she was Jewish, then Agudas Achim Cemetery looks to be a likely bet.
Finding a person's burial place can be very difficult in some cases since there is no centralised repository or records. It can be hit or miss what kinds of records were kept and survive, and in cases where there are no online records you may have to contact the relevant cemetery directly.