Where would you stay or four days - marais area or eiffel tower area or some place else?

I recently stayed at Hotel le Regent (Sept) and I found the location was excellent. It is on the border of the Latin quarter and St Germain, 2 blocks from a metro stop and walkable to Notre Dame and St Chapelle.

Rooms are small. The neighborhood is full of restaurants. Lively night scene, but rooms remain perfectly quiet.

Well under your budget.

We stayed in the St Germain area also. We walked everywhere and were close to the metro. We only used it to go to Versailles.
Our hotel was K+K Cayre St. Germain Pres, Paris.

The Eiffel Tower area is on the western edge of Paris and isn't close to anything else you'll likely want to visit. It's also not particularly well served by the métro. Either St. Germain (no "e") or the Marais, even the Latin Quarter.

Not the Eiffel Tower area which is far from most of the things you want to see in Paris on a first short trip. The Marais is fine if entirely touristy but the Latin Quarter and St. Germain are also good locations to be walkable and IMHO a bit less entirely overrun with tourists all -- they are also touristy. At least there is some normal shopping and living possible. The Marais is boutiques and vacation apartments. But beautiful. And well located. You will probably love it for a first trip.

Paris wonderful because you can walk or take public transit virtually everyplace - you simply can't go wrong, wherever you go., So, it's really question of the type of neighborhood you want -- simplistically - the Marais is young and trendy and very busy, with the Picasso Museum, Carondelet, Place des Voges and Notre Dame right there (yes, I know that Nore Dame is not in the Marais but it's an easy walk); the Eiffel Tower area is much quieter and, depending on where you are, more residential - and there you have the Invalides, the Quai Branley and the Roidin. Personally, we like too stay near the Luxembourg Gardens, at the Luxembourg Parc (ask for a room facing the Senate) because we love to walk in the gardens, attend concerts at St Sulpice and it's central enough to \walk to Notre Dame or to the Rodin (and public transport is very good). Everyone has a reason the stay where they do!

We like to stay in the very center of Paris on on Ile St. Louis. It is right in the heart of Paris and about as centrally located as can be. It's right behind Notre Dame, a metro stop is close by, and there are several places to eat on the main street.

There are a number of hotels on the island. We've stayed at Hotel des Deux-Iles and were very pleased. They also have a sister hotel on the island.

If you decide to stay on the island, we can tell you about a several places to eat.

We're staying our final week at an apartment in Vincennes, near the Bois de Vincennes. Beautiful, tranquil, convenient to everywhere in Paris via the Metro, and much less expensive. It's another option, though admittedly not for everyone.

Earlier this month we stayed at Hotel Des Saints Peres in St Germain and loved it. On a quiet street, easy walking to restaurants and shopping. Probably a 20 minute walk to Norte Dame.

Not sure if it meets you budget, but a wonderful place.

https://www.esprit-de-france.com/en/hotels/hotel-des-saints-peres/presentation-des-saints-peres

We just stayed at hotel left bank in St Germaine and it's a nice hotel, good beds, and good location.