Hotel near Versailles?

How many nights, where are you arriving from, departing to?

Without more info, stay in central Paris.

Stay in Paris and make Versailles an all-day, day trip. You really can't do what you each want in one day. Notre Dame and Ste. Chappelle are a long morning or afternoon combined. Versailles is not in Paris. However, if you only have one day, get the earliest entry to Notre Dame possible. Likewise St. Chappelle (a relatively short walk from Notre Dame). When you finish up at either of those places, take an afternoon train to Versailles to stroll around the gardens before they close. You likely won't have time for the chateau interior. Really, a day like this sounds exhausting and miserable to me and physically difficult. The logistics (you have to make reservations for all three places, though Notre Dame is easier), and coordinating them with enought time to change locations won't be fun.

I second the advice to stay in Paris and make a day trip of Versailles. There's really not a ton to do around Versailles other than the Palace; whereas Paris is well, Paris.

Thank you for kind replies and great advice. We do have a few days to see things and have visited Paris once before. Planning to go see Notre Dame and St Chappelle early one day. Did not realize you need tickets for Notre Dame, so will look into that!

My daughter and I were in Paris in April. Versailles is an easy hour “ish” ride from Paris via the RER. The Versailles station is then a short walk to Versailles - just follow the crowd of people walking out of the station - about a 10-15 minute walk. We had an early lunch in town and then spent the rest of the day at Versailles. I would note that leaving Versailles, the train was quite full, but we left Versailles shortly before it closed.
Unless there are other things you are looking to do in the town of Versailles, I do not think it would be worth spending the night there.

Mook,
You do not need tickets for Notre Dame if you are attending mass. There is a separate entrance for those going to services. Tickets for ND are available 2 days out. Apparently the lines for entrance move quickly, even for non-ticket holders. There is no time limit for staying inside, but earlier in the day it is less crowded. The area where mass is being said is closed off to tourists, naturally, out of respect for the mass.
Ste. Chappelle lines move more slowly, and the security line can be tedious, but that is (IMO) because it is so close to the govt. buildings/courts, etc. I haven';t been to ND since the restoration, but don't miss it. And Ste. Chappelle is a must-see also (IMO). It is uniquely beautiful. Someone here suggested going upstairs to see the chapel first, before seeing the downstairs (entry) level. That is an excellent suggestion. Enjoy!