Paris; Look up Marignan Hotel, rue de Sommerard. Great website.
Budget, clean, quiet, basic, but have started renovating, very close to Notre Dame Cathedral & river (2minute walk), in Latin Quarter,
Breakfast included, free laundry, use of kitchen. I took the shared bathroom option as it was cheaper and shared with only 1 other room, who I never saw. No lifts, so pack lightly, 5 floors, ask for a lower floor when you book. Great value for Paris. Safe area, very central, lots of restaurants. Fantastic location. Single 55 euro.

If you like to walk, any part of the city will do. Paris itself is only a few miles across.

The 5th and 6th probably look more the way you expect Paris to look than the 7th, and will have a younger crowd and more tourists. The 7th is very quiet apart from the Eiffel Tower. Low-numbered arrondissements are more central than high-numbered arrondissements. Safety is not generally a problem for anywhere within the city limits, although some areas can be a bit seedy late at night.

oh, if you don't already understand that... the arrondisement numbers go in a spiral (like a snail) starting with 1 in the center of the city and going outward and around and around. A,lso when you see a postal code the last two digits give you the arrondisement number.

I never went to Paris alone but I love the Latin Quarter. I stayed in Hotel Le Petit Belloy Saint Germain. It was clean and well located.

http://www.petitbelloystgermain.com/index.html

Have a good trip!