Recommend Oaxaca? Absolutely, but not for the cheese (you can pick that up in any Mexican supermarket). I stayed a few days in a charming small hotel called Las Golondrinas (full of flowers, great place to bring your significant other), but there are plenty of other hotels.

Oaxaca mole is marvelous: http://www.foodrepublic.com/2012/08/15/the-7-moles-of-oaxaca/

Also be sure to try the chocolate:
https://missionchocolate.com/blogs/travel-blog/16817439-cacao-and-chocolate-in-oaxaca-mexico