Paris

I suggest you get Rick Steves' Paris guidebook and review it yourself because the number of options is enormous.

August is peak tourism season in Paris, so you may want to book something soon.

Since your sights are not located close to each there's no one neighborhood that's going to be totally convenient for all of them. On the other hand any place in central Paris (the lower arrondisments) that is near a metro stop (particularly one with RER connections for Versailles) will be convenient. You can get anywhere in Paris by walking, bus, metro - it's pretty easy to get around.

For first time visitors most people recommend hotels in the 4th,5th, or 6th arrondisments as close to the river as possible and close to metro stops.

I don't have any specific recommendations for hotels but I'm sure you'll get some good suggestions. Or you could do a search on here for Paris hotels as there have been many many threads on the subject.

Yes, a ditto for Wo in Paris. August is actually NOT high season in Paris for tourism. There are definitely still tourists here, but not as many.

What is budget in euros... I usually stay in cheap to moderate hotels in very central areas.. but then I do not know what you consider well priced or what expectations you have for the type of hotel you want.

I look for three basis must haves:

Clean
Air conditioning in summer
Good location.

I accept that in my price range hotel rooms will be very very small.

I do not book for décor or services ( I do not require room service or a concierge )

I find most of my rooms for between 100-140 euros.. sometimes a bit more , sometimes a bit less. Some hotels do offer special prices in August for the reasons stated by woinparis.

Affordable means different things to different people and you probably know that Paris is one of the more expensive cities to stay in. Looking through hotel listings will help you make a choice and the RS listings are as good as they come. Nancy has suggested looking in the 4, 5 and 6 arrondissements. I'd add the 7th to that list. It includes the Eiffel Tower, Rodin Museum, Orsay Museum, Invalides and is just across the river from the Louvre.

You'll undoubtedly be using public transportation as well as your feet to get around, so getting to tourist attractions shouldn't be a problem wherever you stay. You'll want an RER stop for getting to Versailles, but the metro can get you to an RER station from anywhere in the city.

You also might want to consider staying in an apartment. "Affordable" Paris hotel rooms are likely to be small (read "very small") and that reduces the fun of being in them. In addition, a hotel room implies eating out, which adds to your cost. We have "room picnics" to cut down on expenses, but they can be very cramped in small hotel rooms. For the two of you, an apartment would not have to be large, but even a small apartment will likely be roomier than a hotel room, and having a kitchen can be nice even if you don't actually cook meals. You might like a kitchen just to store fruit, bread and wine and maybe even make coffee. Even in a small apartment, you can stretch your legs and relax better than in a small hotel room.

We'll be in Paris in August, too. I hope your stay is wonderful.

Much thanks for all the comments. Very helpful. Knowing the various arrondissements and their proximities is also very helpful. 3 or 4 star priced 150-200 eu would be a preferable range however we are also open to an apt arrangement. Concierge or other hotel services are not necessary. Again, thanks to you all.

Don't just limit yourself to lodging endorsed in the Rick Steves' Guidebook. Because his books are popular and he can only recommend a limited number of places (it's just a guidebook, not a comprehensive list of all lodging in Paris), Rick's places fill up fast with North American tourists, some of whom start to panic when they can't find an available room in one of his recommended hotels.

Do some research on a site like booking.com and see what is available in your price range with the amenities you might require (ex. A/C, WiFi, breakfast). You don't need to book your room through booking.com if you can find a cheaper rate elsewhere (like the hotel's direct website), but booking.com is good to see photos and read reviews from people who have actually used the site to book and pay for a room at the hotel, as opposed to TripAdvisor where anyone can publish a fake review.

You can filter your results on booking.com based on the "Arrondissement" you want to stay in (ex. 4, 5, 6 - you can find descriptions of each arrondissement online if you go to Wikipedia and do a search. The descriptions will tell you what points of interest are located in each neighborhood. If you want to get to the places you listed, look for something relatively close to a Paris Metro stop. You can get to Versailles via the RER C trains, so if you stay someplace near the RER stop, all the better for you in terms of convenience.

If you want something larger like an apartment, but with some of the amenities of a hotel (24/7 front desk staff), you can look into an apart'hotel. A chain like Citadines offers multiple locations throughout Paris and has offerings from studio apartments up to 2 bedroom units - all their units come with apartment style perks such as a kitchen, washer/dryer, etc.

For me the 4th, 5th & 6th Arr. I look for a hotel or apartment around the Saint-Michel Metro/RER stop. From here you can catch the RER-B, North/South & to CDG. RER-C, East/West-ish & out to Versailles. Metro-4, North/South. Walking distance to Notre Dame, Saint Chapelle, Luxembourg Gardens, the Louvre.

I've booked a lovely apt. for 2 in Paris on Airbnb for $100/night. This will be the 3rd place we have stayed with them. I always read the reviews before booking and choose something that has 4 stars. Many times the owner is nearby and you can meet them and get more info about the neighborhood. Search Airbnb by arrondissment. Have a wonderful time.

Last year we stayed at Hotel St. Germain http://www.hotel-saint-germain.fr/uk/index.php and found it ideal. Air conditioned, beautiful, and well located. Also, it included a very nice breakfast, which saved us approx. 40 Euro a day for our family of 4. The staff was extremely helpful. This year we have booked farther east, nearer to Notre Dame, to be closer to the Sorbonne where our daughter will be studying. We have booked at Le Relais Médicis at 5 Place de l'Odéon. I hope it will be as good as Hotel Saint Germain. In my (admittedly limited) experience, anywhere between these two locations gives good access to most of the "top" sites.

"Affordably priced" is relative. The French consider themselves to be a first world economy and have social policies taking care of workers.

We were happy with the Hotel Jeanne d'Arc which I believe was on the RS guildbook list.
http://hoteljeannedarc.com/
Good location, helpful staff and and within my budget. Convenient access by Bus #69:
http://www.parisperfect.com/blog/2012/09/the-69-bus-see-all-the-top-sights-in-paris/

We stayed at "Hotel Saint-Louis en l'Isle" last fall and I really loved the location (on the isle a stone's throw from Notre Dame). I also thought it was reasonably priced. I would stay there again if I were returning.

The first time we were in Paris we stayed in the Rue Cler neighborhood and that was fine too - but I prefered the location of the last place.

Echoing others, the most important thing is to be close to public transportation. My first trip to Paris, I stayed at the end of line #4, (Port d'Orleans) and I spent a LOT of time traveling between sites. The second trip, we were much closer, right between the 6th and 7th, only 0.3 mile from the Orsay and Louvre, at Hotel Montalembert. It was a bit pricier than we would normally spend, but the location was well worth it. (There's a huge Monoprix grocery store literally across the street, which we used to stock our little fridge with late night snacks and wine while we watched the Eiffel Tower light up from our room!). I do highly recommend the hotel - it was wonderful! We only used transportation when we went to Montmarte and walked everywhere else. What you spend to stay closer to the river is saved transit costs and transit time. Well worth spending a little more to be centrally located to some of, what I consider to be, the main sites; Louvre, Orsay, many churches, etc. Enjoy your trip!

Hi Montana travelers, I have stayed in Paris in different accommodations (hotel, apts) in different arrondissements. I have always made all my own arrangements with air travel and lodging. I'm going again next August for my 60th b-day because Paris is my #1 city! Anyway I was reading my R.S. book and he suggested using a company like Delta Vacations. I've been pouring over the site and they seem to have numerous places to stay in different price ranges. When I find one that I like I look on their site or trivago just to get an idea. The only thing it's with hotel and airfare. For a 1st time traveler I too would suggest 4,5,6 & 7 arrondissements. Enjoy

Thank you. Yes we are looking for a VRBO during the dates of Sept 12-20.

A new law was passed this July which will require all vacation rentals to comply with city regulations before a registration number will be issued by the city. If the rentals do not comply, they cannot be listed on the internet, as their IPO addresses will be blocked.
The law will begin to take effect in mid-September 2016.
Not certain if I would risk booking an apartment through an individual or agency until the dust settles.

The star system in Paris is not the same in other countries, and reflects amenities such as elevators, breakfast rooms, handicap access and other things. Your budget is perfectly adequate for a nice hotel room in the center of Paris. Look in the Latin Quarter - Postal Codes 75005 and 75006 - which is the area most people think of when they imagine what Paris will be like. If you require a kitchen, Hotel Residence Henri IV is a very nice choice, in a great location for walking and transportation.

Also, since it's pretty obvious that you don't know where things are located - and presumably how to get to them - a front desk staff will be invaluable.
If you rent an apartment, you'll have to figure things out by yourself, which is a tremendous waste of time and energy.
A hotel will have air-conditioning. Apartments in Paris do not.

Something to check is the MIJE youth hostel. It's well located and they offer double rooms for a pretty decent price. I'm staying there in September, but just renting a bed as I'm traveling solo.