If you decide to consider a hotel in the end, I really enjoyed the Atarazana at the edge of the Zona Colonial. It’s a redone house from around 1860 and has a lot of style. It was renovated by one of the co-owners who is an architect and you see the elements of fashion throughout. An unbelievable breakfast is included. I walked everywhere I needed to go in that area and it’s a block from the Alcazar. You can’t cook for yourself which is my definition of an apartment, and may be more than you want to spend but you may get a discount if you pay cash or if you’re staying for as long as 10 days.
I heartily recommend it.