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We had a good deal to the Hotel des Artes in Montmartre, near the Sacre Coeur. The nearest tube stop is at the Moulin Rouge so a few mins into central Paris, but a fab location for cheao and atmospheric restaurants around a square with artists etc all plying their trade.
I don't know a hotel or B&B, but we stayed in a self catering apartment with these guys www.parisautrement.com/ and it was lovely and really cheap (though you wouldn't think it from how gorgeous they are). They are in the Marais, which is really central and only a few blocks from the Seine. They can have romantic breakfasts in bed instead! and put the money they save towards a meal out.