Hotel Britannique is where my 80 something parents have stayed twice and it's super central and they loved it. I'm a local so hotels aren't my thing but I know neighborhoods.
If you are a first time visitor or just want to be centrally located in Paris then anywhere that is within a 5-10 minute walk either on the north or south side of the Seine River starting from around Île-Saint-Louis in the east to around Place de la Concorde in the west would suit you. This is prime territory in central Paris and you'll never be more than a block or two from métro stations, cafés, stores, restos etc. and just about anywhere within this zone will give you that “Paris feeling” (quaint, charming, old world, etc., pick your superlative). The most popular areas (and that's not a bad thing) within this zone would be the Marais, the Latin Quarter and Saint-Germain neighborhoods and since these are vaguely defined neighborhoods that you won't find labeled on a map I'll try to point out some rough boundaries that would be considered the prime tourist locations in these neighborhoods.
The heart of the Marais that interests most tourists would be bordered by rue de Rivoli and rue Saint-Antoine on the south, rue du Renard on the west, rue Rambuteau and rue des Francs Bourgeois on the north and Blvd. Beaumarchais and Blvd. Henry IV on the east. The entire Marais extends beyond these borders (I prefer the northern part of the Marais north of here closer to Place de la République) but my parameters have defined the heart of this neighborhood, though certainly you could justifiably argue these parameters.
The heart of the Latin Quarter and Saint-Germain neighborhoods (adjacent neighborhoods) could be defined by the Seine river on the north, rue des Fossés Saint-Bernard on the east, rue des Ecoles and Blvd. Saint Germain on the south and rue des Saints-Pères on the west. Again, I've only defined the heart of these neighborhoods and there are certainly lovely and conveniently located places south of Blvd. Saint-Germain that lie within these neighborhoods, such as around Luxembourg Gardens or near the Panthéon, for example.
Get a good map of Paris of the scale of about 1:15,000 to orient yourself and a good map of this scale will show all the streets and street names, major sites, attractions, monuments, museums, parks and gardens as well as the location of métro and RER stops. A handy map booklet that fits easily in a purse or backpack is called Paris Pratique Par Arrondissement, L'Indispensable. It can be bought on-line or easily found in Paris in touristy souvenir stores, news/magazine kiosks you'll see on the street, bookstores, large supermarkets, department stores (like FNAC) and sometimes the tabac stores (usually in touristy areas) among other places.
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