In addition to the sanctuary (which may include narthex, nave, choir, chancel, and apse), the large worship area, you’ll have a wide variety of other rooms in a church building or complex.
Obviously, any church with indoor plumbing will have restrooms for its members’ use.
In a church that does communion services regularly, there will be a sacristy located adjacent to the chancel area, which is basically a storage-and-preparation area for the communion elements and vessels, and other “ecclesiastical tableware” like a missal stand, collection plates, ciborium, pyx, etc.
Adjacent to the sacristy will often be a vestry, which has nothing to do with the governing board for the church that may also be called by that name, but is a place where the ministers, acolytes, choir, etc. put on their vestments.
As Tom~ noted, there will be a variety of religious education classrooms. The church is also likely to have a library including books of interest to parishioners, which is often where an adult religious education class meets.
Typically, the clergyman will have his own office, adjacent to which may be one or more offices for a secretary providing him support and for various members holding church offices. (E.g., the church treasurer may need a place to keep and work on his financial records at the church.)
Most churches of any substantial size will have a small chapel suitable for private devotions and small-group services, separate from the large sanctuary.
There is generally a large room suitable for church dinners, parish meetings, non-worship entertainment events, etc. This may be beneath the sanctuary, in which case it is the undercroft, or it may be in another wing altogether. Adjacent to this room is probably a large institutional-size kitchen.
Pre-Renaissance churches in Europe will often have a Baptistry, a separate room or building where baptisms are performed. With the Renaissance and Reformation, it became the custom in both Protestantism and Catholicism to have the accouterments needed for a baptism in the sanctuary itself.
There is sometimes a separate room for the choir’s rehearsals.
The church may have a variety of social ministries which need their own facilities. For example, an inner-city church may sponsor a health clinic for its poor neighbors. It may provide facilities for charitable or service organizations: a counseling center, AA, a crocheting club, a gay youth meetingplace, etc. Their needs will be as various as their identities: a food bank, for example, will need dry secure storage for its foodstuffs. A teen center may need the equivalent of a family room with couches, tables, TV, and perhaps a pingpong table or similar recreational furniture.