[One, Two, Middlesboogie]

Here's a riddle. Solve it to find what city I live in.

The first letter is in LLAMA but isn't in MANGO.
The second is in TOAST and not in SODA.
The third is in FINGERNAIL but not in CUTICLE.
The fourth isn't in ZEBRA nor is it in CAMEL.
The fifth is the same as the one that came before this one's penultimate precursor.
The sixth is that letter of the alphabet whose number is the product of the first and fourth primes.