My fiancée and I often take trips to the Mexico City area to go watch lucha libre shows (that mutual interest is how we met). We've gotten the "Mexico City is dangerous" spiel from her family, which is amusing to me because they live in Ciudad Juárez. [For what it's worth, I saw shows in Neza and Juárez this month, and the area around the latter felt much less safe to me.]

I've been pretty much all over the DF area to see shows (including in Tepito). Though I wouldn't go to most places alone and wouldn't make a habit of going to Tepito every trip, our group has never been bothered. (That said, we're always with someone local when we're going to the more esoteric/unfamiliar places, and usually arrange to have a safe ride immediately coming out of the arena.) You certainly can't be cavalier, but that's good advice in any large city.

When we're in DF, we invariably choose a hotel near Reforma 222 -- it's a nice area, and there's a tour bus (Turibus) that stops there and has several routes for exploring various attractions. Looking at the Turibus routes is a decent way of getting ideas of what to see, actually.

I would probably be in Mexico City every second or third weekend if I had the money to retire right now and travel that often.