Would appreciate any help with choosing hotels in Zurich. I will be there at the end of July. My priorities are location near main tourist areas (including train station), cleanliness, quiet rooms, and rooms that are not overly small or low ceilings. My price point is to stay below $300-$325/night in a 4-5 star hotel. I am considering Hotel St Gotthard ,Hotel Glaernishchof, Helmhaus, and Glockenhof. Any comments on these? Any other suggestions?

I am about to post a similar question. I'll be visiting Zurich for the first time in early September and booked a cancellable double for 3 nights at Hotel Rossli for a little less than $200/night USD, including breakfast and taxes. But I'll be interested in other recommendations...

I've stayed in two of the hotels of Redwood27's list and a few more - but mostly as one night stays on business trips.
Since I literally used most hotels just from 10-7, my experiences are not really relevant for those who are looking for a nice place to spend a few nights on vacation.

Just a few generic remarks:
Hotels in historic buildings are usually less standardized re. size and shape of rooms than those newer made-for-purpose hotel buildings. So one room can be quite spacious with a big bathroom, and the room next door smaller with a tiny bathroom. Or higher ceilings on the lower floors, and low ceilings on the top floors. If you had special needs or strong preferences, I'd double check with the respective hotels if they can guarantee a certain feature.

Personally, I prefer to stay in the Langstrasse quartier - if only to have a few more options re. pubs or eateries at night that do not incur such a massive sticker shock than those closer to Bahnhofstrasse or in the Niederdorf (Old Town). There is still enough of a sticker shock when going out for drinks or dinner in Switzerland anyway
But I understand that the Langstrasse neighborhood lacks a certain "swissness" that most people expect from staying in Zurich.
Nevertheless, I think that GinnyJo's Hotel Rössle is a pretty good deal for less than $200/night.

booking.com

Pension St Josef. I have stayed here twice. I have also stayed at the posh Baur au Lac, but it is way beyond your budget.

Thin🍷

I also stayed at the St. Josef and was very pleased with it, but I would not call it a 4 or 5 star hotel. And when I was there, it didn't have AC in all (any?) rooms, so if that's important, check into it.

Thanks for the rec for Pension St Josef -- unfortunately it is unavailable for my dates but it looks like a nice option.

Did you try the Motel One? Don't be put off by the name, these are well regarded properties. We've stayed in the Zurich one a few times, usually when we have a flight the next day and don't want to stay at the airport Radisson, which is going steadily downhill, IMO, it's like they've lost the will to live knowing The Circle's Hyatts will crush their business next year anyway...

We're staying at the Motel One again in June. In late July, a king room with balcony will run about 225 CHF per night, wifi and breakfast included. Rooms have AC.

https://www.motel-one.com/en/hotels/.../hotel-zurich/

Thanks for these suggestions...

We'll be going to Zurich next year... the Hotel Rössle looks good except for the no a/c thing... in July we'll need a/c for sure just to be safe since we always bring a heat wave with us.