What you need is a conditional value list. The relationship between schools and places can serve to filter your values to just those for schools or you can use a stored/indexed calculation field in places that only returns a value if the "place type" is "school".
There's a lot of overlap between the first two links so you can read one and skim the other. The demo file gives you several examples of different conditional value lists so you can examine them to see how they are set up. If you are using FileMaker 12, you can open this demo file from your File menu to get a converted copy of the demo file that you can examine in FileMaker 12.
The last link discusses how to set up a chain of conditional value lists where the value selected in each conditional value list controls the values listed in the next value list.
Forum Tutorial: Custom Value List?
Knowledgebase article: http://help.filemaker.com/app/answers/detail/a_id/5833/kw/conditional%20value%20list
Hierarchical Conditional Value lists: Conditional Value List Question
Feel free to post follow up questions here if those links aren't enough to get your value lists working correctly.
A value list automatically only shows each value one time.
Just use the field that contains the school name in your value list. Even if that table is not even related.
That would be the Places::Name field I believe.
One question: Why isn't the school name stored in the schools table?
I would believe you would create 1 record for each school in the school table. And then relate that to the places using the School ID.
@PhilModjunk - Thanks for the links, I'll be sure to check them out. @DaSaint - Unfortunately I can't simply use the Places:Name field because, in addition to the all the schools, the Places table contains many records for places that aren't schools. I don't want the non-schools to show up in the value list. I don't store the name of the school in the Schools table because I only want the name of a place to be stored once in the database. For example, I can have both a school and a rec center with the same name and location. I'll have one record in the "School" table and one record in the "Rec Center" table, but both will pull their name and mailing address from a single record in the "Places" table. That way, if the name changes (and it occasionally does) I simply change the name once in the Places table and it is updated for both the School and the Rec Center records at the same time.
Ok, I see. In that case PhilModJunk's suggestions are spot on.
Let us know if you can't figure it out.