jdavid05,
I recommend exactly what rborchert suggested. If you are only working with 1 layer you can do one of two things. You can either select by attribute all the features that are a hospital and export them to a new layer, then do the same thing with the airports, creating two new layers, which will allow you to turn off the original layer without turning off your hospitals or airports.
Or, if you have an attribute in your table that tells you what the location is, "hospital, airport, other", then you can use the category symbology and add only the hospital and airport attributes, then uncheck the all other features option to display just those the data you want on your map.