4 Nights in Paris

"Condos" are not legal in Paris. Neither are "vacation apartments".
It's not worth the trouble to track down one of the 200 legal apartments in Paris, vet the owner, stock the apartment, etc for only 4 nights.

You need a nice hotel, totally do-able for under 400 EU (about 400 $) per night.
Google the map of Paris.
Look for the nearest green space - Luxembourg Gardens will probably be what you're looking for.
Use the "search nearby" function.
Enter "hotels".
Book your room.

Stacey, don't forget the monthly travel group meeting in Larkspur, second Saturday -- lots of Paris fans there.

Stacey~
I have used the company, Vacation In Paris. It operates out of the US (NJ) and a very reputable company. They have apartments throughout the the city , some in quite, quaint neighborhoods. www.vacationinparis.com

Hope this helps - Jane

We found a beautiful & restful hotel in the Latin Quarter in the 2014 edition of RS guidebook. Hotel des Grandes Ecoles, about a 15-minute walk south of Notre Dame Cathedral. We would have happily stayed a month there!

Their reservation system is a bit tricky because you have to wait until 4 months before your desired check-in date. Since you're going in January, it should be possible for you to book. See
https://www.hotel-grandes-ecoles.com/

A friend recently stayed in an apartment in Paris, I believe thru AirBNB but I'm not sure. It was awful because the toilet backed up and they weren't able to get the owner to fix it for 3 days. Seriously, they had to plan their use of public restrooms and restaurant lavatories for 3 days. I suppose this type of rotten luck could also happen in a hotel but they'd probably move you to another room if so.

Hotel Luxembourg Parc in 6th. Quiet. Small. Across the street from Luxembourg garden.
Under 400.

If Paris seems claustrophobic, a Paris apartment will, also. With only four nights and being your first time in the city, you should consider a hotel. In addition to Luxembourg Gardens, other large green spaces are Parc Monceau, Parc Monsouris, Le Jardin des Plantes, and Le Jardin des Tuleries. There's the Buttes Chaumont on the east side of Paris, but the surrounding neighborhood is different from all the others mentioned. There are smaller green spaces everywhere in the city, even behind Notre Dame, as well as hidden green spaces, such as petanque courts in an empty lot on Montmartre, that are wonderful to discover. Hope you can overcome your claustrophobia and enjoy the city.

Paris in January should not leave you feeling claustrophobic at all! I've done Paris in June, October, April and it's just fine. Paris is a fantastic city - elegant and absolutely breathtaking to visit. You've got a hotel budget that will give you lots of options.

Stay somewhere central - not away from the hustle and bustle - you'll find it easier to get around to sites and you'll see that there's lots of charming little streets, full of restaurants and cafes, which are fun to wander.

If you want quiet and peaceful, and you decide to stay in a hotel, make sure you request a room on the courtyard side when you reserve online. We stayed at the Hotel Londres Eiffel in the 7th, just a 5-minute walk from the Eiffel Tower. It's on a quiet one-way street but I requested a courtyard room anyway because I'm a light sleeper even with earplugs. That hotel cost €200 per night for a room for 2 people in 2012; I assume prices have gone up a bit since then.

In April this year we stayed at the Hotel du Levant in the 5th where again I requested a courtyard room. This hotel is on a busy street in a busy neighborhood; the streets get very loud after dark but we heard nothing from our room. I can't remember off the top of my head how much it was per night for a room for 2 people, but it was cheaper than the above hotel. The included breakfast is delicious and the staff are helpful.