diff --git a/moto/rds/models.py b/moto/rds/models.py
--- a/moto/rds/models.py
+++ b/moto/rds/models.py
@@ -387,6 +387,8 @@ def __init__(self, **kwargs):
         if self.backup_retention_period is None:
             self.backup_retention_period = 1
         self.availability_zone = kwargs.get("availability_zone")
+        if not self.availability_zone:
+            self.availability_zone = f"{self.region_name}a"
         self.multi_az = kwargs.get("multi_az")
         self.db_subnet_group_name = kwargs.get("db_subnet_group_name")
         if self.db_subnet_group_name:
@@ -495,6 +497,7 @@ def default_db_parameter_group_details(self):
     def to_xml(self):
         template = Template(
             """<DBInstance>
+              <AvailabilityZone>{{ database.availability_zone }}</AvailabilityZone>
               <BackupRetentionPeriod>{{ database.backup_retention_period }}</BackupRetentionPeriod>
               <DBInstanceStatus>{{ database.status }}</DBInstanceStatus>
               {% if database.db_name %}<DBName>{{ database.db_name }}</DBName>{% endif %}

diff --git a/tests/test_rds/test_rds.py b/tests/test_rds/test_rds.py
--- a/tests/test_rds/test_rds.py
+++ b/tests/test_rds/test_rds.py
@@ -2019,3 +2019,39 @@ def test_create_db_instance_with_tags():
 
     resp = client.describe_db_instances(DBInstanceIdentifier=db_instance_identifier)
     resp["DBInstances"][0]["TagList"].should.equal(tags)
+
+
+@mock_rds
+def test_create_db_instance_without_availability_zone():
+    region = "us-east-1"
+    client = boto3.client("rds", region_name=region)
+    db_instance_identifier = "test-db-instance"
+    resp = client.create_db_instance(
+        DBInstanceIdentifier=db_instance_identifier,
+        Engine="postgres",
+        DBName="staging-postgres",
+        DBInstanceClass="db.m1.small",
+    )
+    resp["DBInstance"]["AvailabilityZone"].should.contain(region)
+
+    resp = client.describe_db_instances(DBInstanceIdentifier=db_instance_identifier)
+    resp["DBInstances"][0]["AvailabilityZone"].should.contain(region)
+
+
+@mock_rds
+def test_create_db_instance_with_availability_zone():
+    region = "us-east-1"
+    availability_zone = f"{region}c"
+    client = boto3.client("rds", region_name=region)
+    db_instance_identifier = "test-db-instance"
+    resp = client.create_db_instance(
+        DBInstanceIdentifier=db_instance_identifier,
+        Engine="postgres",
+        DBName="staging-postgres",
+        DBInstanceClass="db.m1.small",
+        AvailabilityZone=availability_zone,
+    )
+    resp["DBInstance"]["AvailabilityZone"].should.equal(availability_zone)
+
+    resp = client.describe_db_instances(DBInstanceIdentifier=db_instance_identifier)
+    resp["DBInstances"][0]["AvailabilityZone"].should.equal(availability_zone)

rds: `AvailabilityZone` is not printed out in `describe_db_instances`
Despite being taken as an argument for `create_db_instance` (and stored in the `Database` model), the `AvailabilityZone` (`DBInstance/AvailabilityZone`) is not printed out in the:
```python
rds.describe_db_instances(DBInstanceIdentifier='arn')
```
call.

Actual response in boto3:
* [create_db_instance](https://boto3.amazonaws.com/v1/documentation/api/latest/reference/services/rds.html#RDS.Client.create_db_instance)
* [describe_db_instances](https://boto3.amazonaws.com/v1/documentation/api/latest/reference/services/rds.html#RDS.Client.describe_db_instances)

This is not a problem for `describe_db_clusters`.

The description of this report is sparse, as I would like to submit a PR right away (this boils down to adding one line in `to_xml` of the `Database` model).

tests/test_rds/test_rds.py::test_create_db_instance_without_availability_zone tests/test_rds/test_rds.py::test_create_db_instance_with_availability_zone
tests/test_rds/test_rds.py::test_create_parameter_group_with_tags tests/test_rds/test_rds.py::test_describe_db_snapshots tests/test_rds/test_rds.py::test_get_non_existent_security_group tests/test_rds/test_rds.py::test_remove_tags_db tests/test_rds/test_rds.py::test_get_databases_paginated tests/test_rds/test_rds.py::test_delete_non_existent_db_parameter_group tests/test_rds/test_rds.py::test_fail_to_stop_multi_az_and_sqlserver tests/test_rds/test_rds.py::test_modify_non_existent_database tests/test_rds/test_rds.py::test_delete_database_subnet_group tests/test_rds/test_rds.py::test_add_tags_snapshot tests/test_rds/test_rds.py::test_delete_db_snapshot tests/test_rds/test_rds.py::test_add_tags_db tests/test_rds/test_rds.py::test_modify_option_group tests/test_rds/test_rds.py::test_reboot_non_existent_database tests/test_rds/test_rds.py::test_stop_multi_az_postgres tests/test_rds/test_rds.py::test_delete_non_existent_option_group tests/test_rds/test_rds.py::test_create_option_group_duplicate tests/test_rds/test_rds.py::test_describe_option_group_options tests/test_rds/test_rds.py::test_modify_tags_event_subscription tests/test_rds/test_rds.py::test_restore_db_instance_from_db_snapshot_and_override_params tests/test_rds/test_rds.py::test_create_database_in_subnet_group tests/test_rds/test_rds.py::test_modify_db_instance_with_parameter_group tests/test_rds/test_rds.py::test_modify_non_existent_option_group tests/test_rds/test_rds.py::test_create_db_snapshots tests/test_rds/test_rds.py::test_modify_database_subnet_group tests/test_rds/test_rds.py::test_create_option_group tests/test_rds/test_rds.py::test_create_db_parameter_group_empty_description tests/test_rds/test_rds.py::test_modify_db_instance tests/test_rds/test_rds.py::test_delete_db_parameter_group tests/test_rds/test_rds.py::test_create_db_instance_with_parameter_group tests/test_rds/test_rds.py::test_create_option_group_bad_engine_major_version tests/test_rds/test_rds.py::test_copy_db_snapshots tests/test_rds/test_rds.py::test_delete_database tests/test_rds/test_rds.py::test_create_db_snapshots_copy_tags tests/test_rds/test_rds.py::test_list_tags_invalid_arn tests/test_rds/test_rds.py::test_create_database_subnet_group tests/test_rds/test_rds.py::test_add_tags_security_group tests/test_rds/test_rds.py::test_add_security_group_to_database tests/test_rds/test_rds.py::test_create_database_with_option_group tests/test_rds/test_rds.py::test_modify_option_group_no_options tests/test_rds/test_rds.py::test_create_database tests/test_rds/test_rds.py::test_create_db_parameter_group_duplicate tests/test_rds/test_rds.py::test_create_db_instance_with_tags tests/test_rds/test_rds.py::test_security_group_authorize tests/test_rds/test_rds.py::test_create_option_group_bad_engine_name tests/test_rds/test_rds.py::test_start_database tests/test_rds/test_rds.py::test_stop_database tests/test_rds/test_rds.py::test_delete_non_existent_security_group tests/test_rds/test_rds.py::test_delete_database_with_protection tests/test_rds/test_rds.py::test_add_tags_option_group tests/test_rds/test_rds.py::test_database_with_deletion_protection_cannot_be_deleted tests/test_rds/test_rds.py::test_delete_database_security_group tests/test_rds/test_rds.py::test_fail_to_stop_readreplica tests/test_rds/test_rds.py::test_describe_non_existent_db_parameter_group tests/test_rds/test_rds.py::test_create_db_with_iam_authentication tests/test_rds/test_rds.py::test_remove_tags_option_group tests/test_rds/test_rds.py::test_list_tags_security_group tests/test_rds/test_rds.py::test_create_option_group_empty_description tests/test_rds/test_rds.py::test_describe_option_group tests/test_rds/test_rds.py::test_modify_tags_parameter_group tests/test_rds/test_rds.py::test_describe_db_parameter_group tests/test_rds/test_rds.py::test_remove_tags_snapshot tests/test_rds/test_rds.py::test_remove_tags_database_subnet_group tests/test_rds/test_rds.py::test_describe_non_existent_database tests/test_rds/test_rds.py::test_create_database_security_group tests/test_rds/test_rds.py::test_create_database_replica tests/test_rds/test_rds.py::test_modify_db_parameter_group tests/test_rds/test_rds.py::test_describe_non_existent_option_group tests/test_rds/test_rds.py::test_restore_db_instance_from_db_snapshot tests/test_rds/test_rds.py::test_delete_non_existent_database tests/test_rds/test_rds.py::test_list_tags_database_subnet_group tests/test_rds/test_rds.py::test_modify_db_instance_not_existent_db_parameter_group_name tests/test_rds/test_rds.py::test_list_tags_db tests/test_rds/test_rds.py::test_create_database_non_existing_option_group tests/test_rds/test_rds.py::test_describe_database_subnet_group tests/test_rds/test_rds.py::test_create_database_no_allocated_storage tests/test_rds/test_rds.py::test_list_tags_snapshot tests/test_rds/test_rds.py::test_get_databases tests/test_rds/test_rds.py::test_create_database_with_default_port tests/test_rds/test_rds.py::test_remove_tags_security_group tests/test_rds/test_rds.py::test_create_db_parameter_group tests/test_rds/test_rds.py::test_delete_option_group tests/test_rds/test_rds.py::test_create_database_with_encrypted_storage tests/test_rds/test_rds.py::test_rename_db_instance tests/test_rds/test_rds.py::test_add_tags_database_subnet_group tests/test_rds/test_rds.py::test_reboot_db_instance tests/test_rds/test_rds.py::test_get_security_groups tests/test_rds/test_rds.py::test_create_db_snapshot_with_iam_authentication