Recommendations for the best hotel that meets our needs

That's $140 per room per night, correct, not for two rooms ?

I use booking.com to filter for price, area, bathroom facilities, breakfast costs, and quality as judged by prior visitors.

In Italy, hotels typically have a free breakfast; in France, they typically don't. You could take care of your #3 "must" by stopping at a local boulangerie for croissants.

I've stayed in that area, but our hotel was more expensive. Looking at "6th arrondissement" on Expedia.com, it looks like L'Hôtel Royal Saint Germain could meet your needs, depending on reading through the reviews, etc.

Yes, sorry, it is $140 per room per night.

The currency in France is the Euro. For anybody checking, at the moment that's around €129 per room.

No guarantee that the exchange rate will be that in June.

I think that that may be a bit tight in the 6th, especially if you include restrictions such as number 3 and number 5.

Look at hotel ste germaine at 88 rue du bac. We stayed there 2 years ago and liked it very much. Also, Relais Medicis at 23 rue Racine. Stayed there last year and like it too. Both near Metro stations, traditional decor and included breakfast.
Finally, you might also consider renting an apartment instead of a hotel. Your cost per night will likely be lower, and you will be able to have some meals in, which also helps on the budget.

Thanks to everyone for your suggestions. It is very much appreciated.

This is a good hotel located in the 6th arrondissement. Included are free breakfast and free Wi-Fi and all the charm you can handle.
You didn't mention your dates, but I would call or email the hotel to find out if there is any availability. I took a glance at www.booking.com, first.
http://www.hotel-saintandredesarts.fr/

This one will tick all your boxes , except there's no free breakfast as that is not the norm .

The rooms are very small , and in cheaper doubles the bathrooms are also very small ( private of course , but many are retro fitted into rooms ).

Location is excellant for all transport options and walking , just off the busy boulevard that separates the 5th and the 6th ( on the 6th side ) but on a quiet side street .

Cheap as rooms are small and no mini fridges , however clean and with good air conditioning .

Cool old cage type elevator or windy steps .
Staff pleasant .

Ha just posted this without Hotel name !!

HOtel St Pierre - Rue Ecole du Medicine ( there are a few hotels in Paris with same name , you want the one on the 6th)

Your budget is low for June in an area that is very popular with tourists. Are you willing to look in the 5th where hotel prices are a bit lower. You will likely not get item 3 in the 6th -- in fact, I encourage you to remove that from your "musts" and be realistic about what your budget will get you during a peak travel month in one of the more expensive parts of one of the most visited cities in the world. Take a look at Hotel de Nesle -- location is in the heart of the 6th and the cost should work though it could be slightly above. Some rooms have private bathrooms. There is no elevator and I can't recall if there is AC (it's not on your list of "must" but I mention it anyway) but I'd bet that there isn't any. I don't love this hotel but that is because to me it is too cluttered and that draws out my desire to clean up and organize and I don't need that feeling on vacation. Another suggestion is the Hotel Clement where a classic double room with AC and a private bathroom starts at 119€ but may be above your budget in June. I have not been to Hotel Clement in a while but a few years ago it needed a refresh and I do not know if it has been renovated recently. If you are willing to go to the 5th, take a look at Hotel Diana and Hotel Excelsior Latin. Good luck with your search and have a great trip.

I like the Grand Hotel des Balcons. They definitely meet criteria 1, 4, 5, and 6. When I stayed there the breakfast was extra, but it was a full breakfast including eggs, not the continental one usually found in French hotels. I don't know if it's included now or not - you could email them to ask. And you'll have to check prices for your dates. Note that they have quad rooms, which will save money if that works for you.

http://www.balcons.com/en/rooms.html

Thanks to everyone for the wonderful suggestions and tips.