hmmm...
...let's see...
record stores, there are not many, they are pretty none exitant actually, but if you like prograssive rock and classic rock shit i can point you to some places.
a place to check out, if only for the amusement of witnessing is "el tianguis del chopo" which is a flea market that's all rock related stuff...not much obscure stuff but if you want to score some mexican edition vinyls by relatively well known bands or t-shirts or punk bootlegs or hard to find movies from all around the world and maybe even hear a local band play there, you should definitely go. it's also a sight the people who go there. the place only sets up on saturdays though.
you should definitely go to the historical downtown, it's pretty cool to walk around and stuff. go during the daytime, though.
there's a ton of cool museums, i'll look for a place online where you can locate all that stuff. and yeah, i've been to leon trotsky's house, that's in coyoacan, a beautiful place.
downtown is like the obligatory turist thing to do (besides going to the pyramids of teotihuacan), there's other places...i'm not really sure what else is "turistic" around here besides that, the museums and the chapultepec park (beautiful place too to walk around).
i'll go look for some kind of directory for you. here you go, just seach around:
http://www.mexicocity.gob.mx/index_EN.html