This was one of my favorite clues. It's a meta-clue, where the answer is the solution!

First, look at the drawing. It's from the scene in "The Matrix" when Neo goes to the Oracle to see whether he is "The One" and while he is waiting in the waiting room, he encounters a Buddha-like child who attempts to educate him. The child shows him a spoon and says "There is no spoon.:"

Next, the writing on the inside of the envelope gives you a hint that this is a meta-clue, containing a quotation from Goedel, Escher and Bach: "The poem contains its own commentary..."

Each of the seven pieces of paper contains a puzzle whose answer is "THERE IS NO SPOON." There is no need to decipher each puzzle. The important thing is how the puzzles were encoded. When you figure out the encoding method on each puzzle, fill in the blanks at the top of the puzzle with the name of the encoding method. Then take all of the letters that have numbers beneath them, and sort those letters into numerical order. That yields the next clue destination.

In the meantime, just for fun, we'll "solve" each puzzle. But we already know all the answers - THERE IS NO SPOON.

The first puzzle is an ASCII code. In ASCII, the upper case letters of the alphabet are represented by the numbers 65 (A) to 90 (Z). For each line, count the number of characters it contains (including spaces) and then convert to the corresponding letter in ASCII.

In the next puzzle, we are given fourteen times of day to figure out. Each of these times of day can be represented by the two hands on a clock which, when positioned properly, also correspond to semaphore positions. In semaphore, the operator holds a flag in each of his hands and then extends each arm in one of eight positions corresponding to the directions N, NE, E, SE, S, SW, W, and NW. It doesn't matter which hand is extended in which direction, so there are sixty-four semaphore positions of which 26 code for letters of the alphabet.  Note below that 6:10 and 2:30 look like the same position in semaphore so they both represent the letter 'E.'

This next puzzle is a Caesar shift cipher ("All Roads Lead to Rome" was a hint). This is a very simple letter substitution cipher in which every plaintext letter is shifted a certain number of letters to the right (or left, same thing if you consider the alphabet a continuous loop) and is replaced by the resulting letter to create the ciphertext. In this case, to make a nice 5 x 3 grid "THEREISNOSPOON" becomes "THEREISNOSPOONX" and then the letters get shifted two to the right to become "VJGTGKUPQURQQPZ."  (The X becomes a Z which is not really part of the solution.)

This next puzzle is an anagram - "HOT ION RESPONSE" unscrambles into "THERE IS NO SPOON." In cryptic crossword puzzles, almost anything can signal an anagram - such as using the words "mixed up" or "scrambled" in the clue. I have no idea what "From unconnected bitter ancient robot" is supposed to mean other than that its acronym, FUBAR, could certainly be used as an anagram indicator.

This next puzzle is a reflection - you can see "THERE IS NO SPOON" reflected backwards below.

It's pretty clear.

R     E     F     L     E     C     T     I     O     N

27   13                  21             6                   11

This next puzzle is in Morse Code - and again the title is a clue. On each line are between one and four people, some of whom are real (these would be dashes) and some of whom are fictional (these would be dots). Each line therefore becomes a letter in Morse Code.

The final puzzle is in binary code. Each word can be converted to a 5 digit binary number (I added with leading zeroes to make it look nicer but you don't have to) and then to a letter. In each word, a capital letter becomes a 1 and a lower case letter becomes a zero. ("Execution Matters" was a hint - Execution = CAPITAL punishment.) The first digit is 2^4 = 16, the next one is 2^3 = 8, the next one 2^2 = 4, the next 2^1 = 2 and the last one 2^0 = 1. The numbers are converted to the corresponding letter of the alphabet.

Finally, to get the answer (our next clue destination), from each of the seven puzzles take the letters that have numbers beneath them, and arrange them in numerical order. And the answer is:

CHABOT SCIENCE AND SPACE CENTER

Clue 6