"I don't like a general rule that the single digit Arrs are more convenient and more central. For example, 7-8 feel way out there for me (and parts of 7-8, very much so) as they are not convenient to the areas and things that I like. Also, aligned with my comment above, the 7e has many huge scale open areas that are beautiful but feel treacherous to walk. But, as always, there are preferences in play here."
I agree I don't care for the 7th or 8th as a place to stay. I know the area you like and its fine as is the area where St.Cirq's hotel is in. As you said preferences play in. And yes, the 11th is big. I also know that since we tend to go in the winter, and one trip a couple February's ago it was very cold. We were staying in the 11th near the Richard Lenoir metro and as we would trek home esp at night, and pass thru the 3rd & 4th, I'd say, if we lived here, we'd be home by now. So yes, it really depends upon where you plan to visit.

Paperfist asks "What about AirBnb?"

Most apartments listed on AirBnB are not legal rentals. If you want to look at AirBNB, examine the listings carefully to make sure a registration number is listed.

Definitely check for the registration number. Although I understand that some apts don't list it publicly because people steal the numbers and use them on their ads. That said, in my recent search for an apt I was pleasantly surprised how many AirBnB and others had registration numbers. Much different than when I looked a year ago. While far fewer apts than there used to be, you can still find legal ones on Airbnb and elsewhere.

Of course, there is no guarantee that the number in the ad is legitimately connected to the apartment on offer.

<<I also know that since we tend to go in the winter, and one trip a couple February's ago it was very cold. We were staying in the 11th near the Richard Lenoir metro and as we would trek home esp at night, and pass thru the 3rd & 4th, I'd say, if we lived here, we'd be home by now. >>

LOL, we said the same thing last August when we were there during an ungodly heat wave and could barely drag our sweaty selves back home from the "center" of the city.

I'm no longer fond of the 7th or 8th, though many years ago we used to stay there pretty often. But I do think lots of people find it easier to be in the single digits because they can see the Tour Eiffel or Notre Dame (or what's left of it) and find it reassuring to be able to walk to the Louvre, the Musée d'Orsay, the Latin Quarter, the boat rides, and all the things they associate with Paris. It certainly took me many trips to Paris to branch out into "new and different" neighborhoods.

"t certainly took me many trips to Paris to branch out into "new and different" neighborhoods."
We've done a fair bit of exploring Paris but in the end, the Gros Caillou neighborhood is where we like to base and it's not because we need to feel "reassured".

A tad over your budget, but if you can swing it the Hotel Brittanique in the 1st is wonderful. The location makes it an easy walk to so much, but the metro is just a block away. We stayed for 5 nights and can't think of any negative for it.

If you don't mind being a bit further away, in the 14th there is the Best Western Bretagne Montparnasse which comes in under your budget. We stayed there on our very first trip and it was great. It is kind of generic, just meaning that there really isn't any charm to it, but we loved it. Just a few blocks from the metro and the staff went above and beyond for us, so much so that I sent a small thank you after we returned home.

My perspective is that 'my' neighbourhood in the 11th around Ledru-Rollin is the centre of Paris.* The Eiffel Tower or the Louvre are not the centre of 'my' Paris.* 7-8 are not an appealing base for me at all.* I'm not really a fan of the Latin Quarter to stay, although it's not objectionable.* Montparnasse, Montmartre...no way.* Not home for me.*

Related to London, it's my Marylebone.* I don't care that there are closer neighbourhoods to the London Eye or 'Big Ben'.* In Barcelona, give me El Born.* Not worried that it's not near Las Ramblas. In Boston, I'll take the Back Bay or South End.* I don't care that you can stay closer to Faneuil Hall.* This is not a snobby 'anti-tourist' view.* I'm happy to visit big sights.* I just don't need to stay right on top of them and I don't think that 'central' is synonymous to where the big sights are located.* I think for most people living in the greater Paris metro area, living in the 11th is extreme central Paris living...it's certainly not suburban living!

<<I don't think that 'central' is synonymous to where the big sights are located.* I think for most people living in the greater Paris metro area, living in the 11th is extreme central Paris living...it's certainly not suburban living!>>

I think for most tourists, though, central IS where the big sights are located. We're not offering advice here to "most people living in the greater Paris metro area."

"My perspective is that 'my' neighbourhood in the 11th around Ledru-Rollin is the centre of Paris.* The Eiffel Tower or the Louvre are not the centre of 'my' Paris.* 7-8 are not an appealing base for me at all.* I'm not really a fan of the Latin Quarter to stay, although it's not objectionable.* Montparnasse, Montmartre...no way.* Not home for me.*"

Perhaps, for you, but the OP was coming to see Paris, not visit "your" neighborhood. As a tourist who regularly visits Paris, while I love visiting vrious neighborhoods and finding new sites, the museums and other "famous" sites are still of interest to me.

Fair point but if someone wants to stay near the Eiffel Tower,, fine. say you want to stay near the Eiffel Tower. Or the Louvre. But just because a neighbourhood is not the closest to the Louvre or the Eiffel Tower, it doesn't mean it's not central. Paris is a huge city so picking one or two sites and considering them as 'the centre' is misleading. Like saying that Georgetown or Dupont Circle is not 'central' in Washington because they are a distance from the Washington Monument or the White House. They are near many sites of interest in those areas and they are in the appealing urban centre - very well catered for with many of the best restaurants and everything else.

An interesting statement to me because I've always thought of Paris, the part within the Peripherique, as quite compact. One visit I'd left my gift shopping until the last day & there was a transit strike. I decided to just walk, from my hotel in the 18th on the back side of Sacre Coeur, shopping my way down to the river & back again uphill with my bags, in my 60s at the time. I think that's about a third of the way across town. I think of London as "huge" & LA & Mexico City but Paris not. It seems to me central Paris could be considered half the town & easily walked by anyone in fair shape.

I stayed at Hotel Original this May and Jules et Jim in June. Without knowing what you're looking for specifically, and considering I was by myself in double rooms and thus they felt plenty big enough, it's hard to recommend them, although I liked them both quite a bit. Hotel Original is less expensive and quite a bit quirkier. Jules et Jim is moire chi-chi and would likely be above your desired price in September, but is worth a look just in case.

https://cimg6.ibsrv.net/gimg/www.fod...f07831764e.jpg
Hotel Original - smallish room, great terrace and view.

https://cimg8.ibsrv.net/gimg/www.fod...432e19933a.jpg
Shower/sink/desk/closet at Hotel Original. Efficient!

https://cimg5.ibsrv.net/gimg/www.fod...0ee9c3527.jpeg
Hotel Original

There is only one reason not to include a registration number on apartment advertisements - the owner doesn't have one. The law requires it be there.

The dishonest do not need to steal numbers, they make them up. Having a number is only half of what makes an apartment a legal rental, it also must not have been rented more than 120 days during the calendar year.

Is there an easy on line way to check registration number against a list to see if it a real number and matches the advertised apartment?

No. That is something that the city inspectors do. Even if you could, the number alone does not guarantee that any given property has been rented under the 120 day annual limit, making further rentals legal.

What you know for sure is that any listing without a registration number is certainly illegal and should be avoided.

What's wrong with the neighbourhood? A bit of a desert at the weekend, but wonderfully close to Parc Monceau etc. Avenue des Ternes for the shops and I see lots of restaurants etc nearby too.