Hi Catherine,
I can't speak to Mexico City, but I recently had a wonderful time in Oaxaca ( Walking in Oaxaca )
There's a number of excellent tours available. I recommend the following:
Art and Chocolate Tour
Margaux is an amazing tour guide and her tour of Oaxaca's wonderful street art was a highlight of my time in Oaxaca.
I highly recommend any tour with Erick and Edmundo (they also provide pickup service to and from the airport). The tour Erick gave my wife and I of the Sunday market in Tlacolula was worthy of a Rick Steves tour.
My wife and I are heading back to Oaxaca in March and we've booked both tour guides to show us Mitla, Mercado 20 de Novembre, San Martín Tilcajete (home of those wonderfully-colorful wood animal carvings) and San Bartolo Coyotepec (know for their black pottery)
One final tour that I was unfortunately too sick to take is Alvin Starkman's mezcal tour. If you love mezcal, this is your tour. He drives you into the countryside to meet local producers and sample their copious wares. Full warning: this is not for the light-hearted. This is not tourist mezcal. This is as real as it gets. Alvin really knows his stuff and is friends with pretty much everyone in Oaxaca, but the mezcals the indigenous people make is industrial strength. One of my friends said it best: "I can't feel my face anymore".
There is SO much to see in Oaxaca that you'll have an amazing time just wandering around.
Enjoy your trip!
-- Mike Beebe