Where do caching servers conceptually fit in my architecture?
Your caching layer sits between Model and View Controller. You should not hit database for needless requests. These requests include in my opinion.


Almost all lookup tables. You read city and state list already. Why go to database again.
Facts used in almost every page. if you show User's detail every page. Hit to Database once and cache it.
Slow queries you can afford to show with some delay. For example you can cache How many orders your customer have and show it without going to database.


Note that Caching does not need to be for database only. For example you may cache messages from mail server, or expensive file parsing operation result also.

Caching is the number one layer which increases speed of application.