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Mexico City is wonderful, the second-greatest city in N America after NYC, although personally I would never stay in Polanco (or the equally rich-but-bland Roma, Condensa, etc).

A US$70 airport pickup is a ripoff: the taxis from the prepaid taxi line at the airport, about $12-18 depending on destination, are not the same as street-hailable taxis and are 100% safe. Returning to the airport, the hotel can call you the same type of taxi for slightly less. Around town, don't go to the nearest hotel, go to the nearest sitio (taxi stand), these are near all major intersections and sights. Sitio taxis are tightly licensed and completely safe.

I agree that Coyoacan is the best area of Mexico City; unfortunately there are no hotels close to the action there. So Centro Historico is the most practical area to stay in. There is a substantial police presence there as well, but it does not seem necessary; Mexico City is as safe as any other big city, and Centro is full of life. On weekends, join the dancers on the west side of the cathedral...

There are many excellent hotels in Oaxaca; there is no single "main hotel". I like the Victoria, an older hotel with a good view from a hill on the outskirts of the center but still only a pleasant one-mile walk to the main square. The fried grasshoppers are excellent: buy a US$1 bag at the market. The ice cream in the market is good and there are many unusual flavors.

In Merida, "the main reason to come" is to see what happens there every Saturday night and Sunday. It's a city-wide party, and I don't mean spring break; it's for the local people.

In Mexico, the simple pleasures are the best. For US$50 and up you can get fake food designed to feed the egos of rich Mexicans and the hygiene concerns of tourists. But for US$2 you can get a seafood tostada at the Mercado de Coyoacan, or a turkey sandwich with mole at the Churreria del Morro (join the long line): this is real food refined by real people and by time and culture, and it will astonish your tastebuds. (And no, it probably won't make you sick. Mexico is far cleaner than a decade ago, just eat where others are eating too.) A US$0.70 coffee at the Cafe El Jarrocho, or a US$1 fruit ice at the Nieves de Coyoacan, will also show you that you don't have to spend lots of money to get the best of the best.