My understanding is that every follower of Islam is required to make a
"pilgramage to Mecca."
 What if they already live in that city, or so closeby, that it's not
really a pilgrimage?
 Is there some other sort of requirement under the pillars of Islam?

Hello pcventures-ga:

Thank you for the interesting question. You might already know that
every Muslim is required to perform five duties (five pillars of
Islam) including a pilgrimage to Mecca. Some of the text forgets to
state that, this condition (pilgrimage to Mecca), is required for all
Muslims BUT if they can financially and physically support such a
visit during their lifetime. It must be noticed that the Arabic word
?Hajj? does not only mean ?Pilgrimage? but the word itself has broad
implications. Please see
http://www.usc.edu/dept/MSA/law/fiqhussunnah/fus5_66.html

For those Muslims residing in the Holy city of Mecca, they are not
required to perform any special duties because of their proximity.
They are just a little fortunate that they reside nearby and can
fulfill this duty (pilgrimage easily).

Two things should be made clear. First, the pilgrimage to Mecca is not
actually a pilgrimage in a traditional sense, it is Hajj. The word
?Hajj? is used in Koran many a times to tell the Muslims that this is
their duty. Never in the Koran, is it written that a Muslim should
carry out a pilgrimage to Mecca but only that a Muslim should perform
Hajj to the House of Kabbah. For example in the Quran, it states that
"..And Hajj (pilgrimage to Makkah) to the House (Kabah) is a duty that
mankind owes to Allah, those who can afford the expenses (for one's
conveyance, provision, and residence)..."
Al-Quran: Surah 3 (Al-Imran); Verse 97. 

Notice the addition of Brackets that are used to tell the non-Arabic
reader, what is the closest meaning of the specific word? Thus, it is
not important that you really have to come from a far away land in
order to perform Hajj. Secondly, it is important to know that all of
the Muslims agree on one point and that is, if someone undertakes a
journey from a far away land in order to perform Hajj, in the
hereafter he/she will be rewarded for their efforts accordingly. This
means that the residence of Mecca will definitely get a reward but the
one who carries out this journey from a distant land may expect even a
greater reward.

It is noticeable that it was difficult to perform Hajj in old days
where there was no transportation. It can easily be inferred that a
majority of Muslims never undertook ?Hajj?. Again, the Koran
explicitly states that you perform Hajj if it is physically possible.
Even then, there were Muslims who traveled long distances to carry out
?Hajj?. Even now, it is not easy to perform Hajj. Saudi government has
limited amount of Visas for the travelers who want to undertake this
Journey. The government is also reluctant to issue visas to the people
who have already performed Hajj, once (it can be performed multiple
times). There are various good reasons for that. Please clarify, if
you want to know, why?

Here is a brief and a good writing on ?Hajj?. 
http://www.wordiq.com/definition/Pilgrimage_to_Mecca?PHPSESSID=3fd4923e69923bb3bcda6a35894a1c18

I am myself a Hajji (one who has performed Hajj). Please clarify if
you are still confused. I know this can be a little confusing. I will
be very glad to answer your questions.

Sincerely,
Leader-ga.

Thank you for increasing my understanding of the Hajj.