The neighbourhood advice you find assumes a stay of indeterminate length. It does not exist. Two nights in Paris and six nights in Paris are different trips, and the right answer flips somewhere between them.
The arithmetic nobody does
A metro journey from the eastern arrondissements to the centre takes twenty to thirty minutes door to door. Say you make three a day — out, back for a break, out again.
Two nights, that is roughly three hours of your trip spent travelling. On a forty-eight hour stay, three hours is a meaningful fraction of what you came for.
Six nights, the same daily pattern costs you nine hours — but across a much longer stay, and against a room that is larger, quieter and cheaper for every one of those nights.
The number of nights does not change the daily cost. It changes whether that cost is worth paying.
Two nights or fewer
Stay central. The Marais, Châtelet, or anywhere within walking distance of what you came to see.
Accept the small room. You will be in it to sleep and to change. Its size is the least relevant fact about your trip.
Do not optimise for value. At this length, the savings are small in absolute terms and the time cost is large in relative ones.
Three to four nights
This is where it depends, and where most people get it wrong by defaulting to the centre.
The question becomes: how much of this trip happens indoors?
If you are out from nine to eleven, moving constantly, seeing things — stay central. The room is a base, not a place.
If there are slow mornings, an afternoon break, a child who naps, or work to do — the eastern option starts paying. You will use that extra space for real hours, not hypothetical ones.
Five nights or more
Go east, or at least out of the tightest centre. Oberkampf, République, Nation, or the quieter parts of the 9th.
At this length you stop being a visitor and start being a temporary resident. You will want a supermarket, a laundrette, a café that recognises you. Those exist in residential neighbourhoods and not in the tourist centre.
You will also want somewhere to be that is not a bedroom. Five nights in a twelve-square-metre room in the Marais is a different experience from two.
The question that settles it
Not "how long am I staying" but: how many hours will I spend in this room awake?
Under ten across the whole trip, take the location and forget the space. Over twenty, take the space and accept the metro.
Most people cannot answer this precisely, which is fine — the estimate is enough. A couple doing museums answers differently from a family with a four-year-old, and both know which they are.
Who this does not suit
If you are here for a fixed appointment — a conference, a hospital, a family address — proximity to it beats everything written above. Ignore the arithmetic and stay close to the thing that cannot move.
If you are arriving late or leaving before dawn, the transport connection matters more than the neighbourhood. Châtelet exists for exactly this.
If someone in the party has difficulty with stairs, the building matters more than the district, and neither the length nor the location changes that.
What we do not know yet
We do not publish rates, and we cannot tell you what a given establishment charges for three nights versus six. Prices in Paris move weekly.
What does not move is the arithmetic. Three metro journeys a day cost the same amount of your time regardless of the season.