I've stayed at three hotels in the Marais that fit the bill:

Villa Mazarin 6 rue des Archives
Hotel de la Bretonnerie 22 rue Sainte Croix la Bretonnerie
Hotel Bourg-Tibourg 19 rue du Bourg-Tibourg

The last one is the priciest of the bunch, probably close to your upper $$ limit. Bretonnerie had a cute room on the top floor with exposed timber beams. Because of the angled roof some of the walls were closer in at the top than at the bottom. Maybe it's not everyone's taste, but I thought it was charming. My room at Villa Mazarin was like a little jewel box. All are close to the Metro, but Villa Mazarin is virtually across the street from Hotel de Ville Metro station.