Everything downtown is centrally located. SF is small and confined, not spread out.
There is no AC in SF, right now it's in the 50s to 60s in the daytime and in the 40s to 50s at night.
You'll more likely need to close the windows and grab a blanket and slippers before you'll need the crank up the AC.
OP, centrally located to what? The wharf? Financial district? Convention Center? Union Square? Please be a bit more specific and help will come. You mentioned the Ritz. Is that the level/price of hotel for which you are looking???
You never need AC in San Fran. Do you know how perpetually windy that city is?
Wyndham Parc 55 is just across the street from the Powell Street BART station in a flat part of town (convenient to transportation) and has A/C in the rooms.
It's a really huge convention-style hotel, but the rooms are nice enough and if there's no convention in town or the hotel isn't pre-sold for an event, it can be extremely reasonable if you check the discounter sites.
Bonus: if the hotel's not full and you're reasonably nice, I've found the staff is happy to accommodate requests for the quieter side of the building, a high floor, etc.