A few years ago I stayed at the Hotel Van Onna and found it to be a pleasant hotel for a fair price in a delightful area of Amsterdam.

However, the local church bells woke me at 3 AM and I could not get back to sleep. It made for an unhappy day of sight-seeing the next day and each day after that. I've always booked other hotels since then.

I saw in the "News" section that the Westerkerk was to undergo a renovation. I'm not sure if this church was the bell-ringing culprit or not.

So, my question is: If I book at the Hotel Van Onna are the bells silent ?

As of now, the bells are still ringing at the Westerkerk and that would be the one causing your issue. I just stayed at the Hotel van Onna in the last week while family stayed in my place and it is a clean, inexpensive, no frills hotel. Did not have a problem with the bells as I had the window closed all the time. Smoking was not allowed in the rooms and this would be a hotel to avoid if you want to smoke. It is definitely not a "party" hotel.
I also spent one night in the Old Quarter Hotel on Warmoestraat and it was surprisingly clean and seemed pretty secure but I would think that during the season it could get pretty loud outside making it difficult to keep your window cracked.

Teleport, the bells as you say, are one of the best thing in Amsterdam, carillons are music to my hears, let you feel the taste of the time, can bring your feelings hundreds years back, and let you feel romantically involved in a place made on men's dimension.