This is a question of grammar.  I will need at least 3 references that
coincide with this specific situation and grammatical application.

The question is in reference to a picture taken outside of a venue. 
The venue is a standard concert type building.  The band was Panic! at
the Disco.

So in a caption for the photo, which of the following would be
grammatically correct :

"Thomas and me at the Panic! at the Disco concert"

or

"Thomas and I at the Panic! at the Disco concert"

The 2nd one is correct.  You do not need a reference, just someone
with basic knowledge of English.

The first is correct, because the foreshortened caption is short for
"This is Thomas and __ at the Panic! at the Disco concert".

'I' is used as a subject, before the verb, as in "I like concerts."
'Me' is used as an object, after the verb, as in This is me and Thomas."

The verb "to be" does not take an object.  In standard English, a
pronoun following "is" or "are" should be in the nominative case  - I,
he, she, we, they, who.

But, of course, most of us say:  "It's me";  even persons who probably
in more formal speech would say:  "It is I."  But I think we do say: 
"That's/It's me" for the good reason that the phrase can be better
understood.

Blame it on the French; they say:  "C'est moi."

sublime1-ga, I hereby forbid you to answer any grammar or language questions.

Also discussed here:

1)"Photo description: 'I/Me and my Daughter in San Francisco' etc.."
http://www.proz.com/kudoz/621462

2) Weekly Grammar Tip (July 1, 2004 - Source: The Handbook of Good
English, by Edward D. Johnson), "It's me or It's I?":
http://www.proofreadnow.com/tips/20040701_tip.html

3) "Oh me, oh my,
Is this me or is this I?"
http://www.upci.org/wap/Assets/E-tips%20archieve/30%20Pronouns.rtf

i find it hard to believe that anyone would caption a photo of one person as:

"I at the Panic! at the Disco concert"

so i would be very suspicious of any so-called rules of grammar (or
interpretations of such rules) that claim it has to be:

"Thomas and I"

however, why worry about the rules of grammar at all?  if "Thomas and
me" sounds better to you, use it.  if "Thomas and I" sounds better,
use that.  it's not like someone won't understand what you're saying.

i have always been of the opinion that language came first, before the
rules of grammar, and such rules are actually an attempt to describe
language as it exists rather than a rigid set of rules you have to
apply every time you want to express an idea. i would say any rule
that requires it to be "I at the Panic..." is, by defintion, wrong,
because it does not describe how english is spoken or written by,
really, anyone.

this philosophy got me in trouble with my english teachers, but it
works surprisingly well once you get out of high school.

but then, sometimes i'm too lazy to capitalize too, so take this all
with a grain of salt.

-cab

Maybe it should read slightly different as well.

For example: Thomas and me at the Disco to see Panic!.

or: Thomas and me at the Panic! concert at the Disco.

or: At the Disco - Thomas and I see Panic!

Cheers

Neither of your examples is a complete sentence. Rules for the usage
of "I" and "me" are not very meaningful when applied to a sentence
fragment which has no verb.

You could say
"This is a picture of Thomas and me at the Panic! at the Disco concert."

or
"Thomas and I attended the Panic! at the Disco concert."

I was there? I can't recall . . . .

weisstho-ga

I think I have misread this.
I thought the band name was Panic!
And the venue was the Disco.

Oops ;)

Thomas and I saw "Panic! at the Disco"

Pinkfreud, your point about applying grammar rules to sentence
fragments is well taken; however, it is generally better but not
strictly necessary to use a complete sentence for a caption (often the
New York Times uses fragments).  I would suggest that the best
approach is to assume that "This is a picture of..." would be the
presumptive preface to a sentence fragment in a photo caption, so you
should use "me" instead of "I".
Anyway, if you really want to do it properly, you should use your name
or "the author" instead of "I" or "me."  Otherwise, your audience
would not really know if "me" is the author of the article or the
photographer.  Normally, photographers write captions because they
frequently work independently from reporters.  The two may not even be
at the event at the same time or they may be in different locations
whithin the event, so the reporter does not necessarily even know what
is going on in the photo.

Here's a very easy way to know whether to use "and me" and "and I:"
Remove the other person from the sentence.

For example, you wouldn't say: "Me went to the disco." You'd say: "I
went to the Disco." So, adding back your friend, you'd write: "Thomas
and I went to the disco."

Kriswrite

Saw an Ad for ~ Panic! at the Disco
CD

Lucky you getting to see them.
I love their music, now I know who they are.

So what happened to the Requests for Clarification that were on this
page? I can't imagine any reason for their removal.

Oops! Ignore that last comment. I was thinking of a different question.

in my opinion, how to use it depends on who you want to emphasize
for example, if you want the listener to know that it is YOU with Tom,
you had better use Thomas (here you should louder your voice) and me,
otherwise use Thomas and I,
well, just some guy talked above, use it that you feel good to speak

we chinese,have no such split,is me,we say: 'shi wo',i am,we say:'wo
shi'.'wo' means me or i;'shi' means is or am or was or be.so you
see,we chinese is a very simple and effective language,very beautiful
too.