Installing and upgrading help

No it won't. 

Try...

ALTER TABLE ADD city varchar(120) COLLATE utf8_unicode_ci NOT NULL DEFAULT '' AFTER address;

I'm not going to ask why you deleted it - it's a required field for users in Moodle

Hi Wendi,

As you want the field to be optional, I would do either of the following (assuming that the table prefix is mdl and that the collation is utf8_unicode_ci):

1. Allow null values

ALTER TABLE mdl_user
ADD city VARCHAR(120) NULL
CHARACTER SET utf8 COLLATE utf8_unicode_ci
AFTER address;

2. Do not allow null values but assign a default value (e.g. the one used in the location settings)

ALTER TABLE mdl_user
ADD city VARCHAR(120) NOT NULL
DEFAULT 'Default_City_Value'
CHARACTER SET utf8 COLLATE utf8_unicode_ci
AFTER address;

If I were doing this, I would go with the second option.