My work colleague is from Paris...here's her recommendations
Places from eatGeneral recommendation is not to eat anywhere that has the menu transalted into English or has photographs on the menu. Her advise is to just wander around and see what takes your eye but to keep clear of eating and drinking in the Trocadero area (around the Eifel tower). Specific recommendations
Cafe Alsace - on the place de mexico. 3 course lunch with wine is around 11 euro's
Cafe Justine - on Rue Oberkamp
Chateaubriand - Avenue Parmentier, this is a bit more expensive and has no choices on the menu (and you need to book).
Head to Metro Villiers and go round the corner to Rue Villiers and there are plenty of lovely authentic restaurants around there.
The area around the Metro Parementier (which is where Rue Oberkamp and Avenue Parmentier is) has, apparently loads of really excellent cafes and bistros and isn't very touristy so it's closer to the real paris.
Must See PlacesGeneral recommendation is to walk as much as you can and just see what's around every corner (there's always the Metro is you get tired)
The Eiffel Tower, obviously, but apparently it's undergoing some refurbishment works - book ahead if you can or go first thing in the morning or late at night.
The backstreets of St. Germain for art galleries etc
Get off at Metro Saint Paul to see the Marry arais and the Place des Vogues (Victor Hugo used to live there and there are musuems in the area including the Picasso museum). There's also the European photography gallery there if you're into Gallery.
From there you can go to a small island called Ile Saint Louis - don't eat or drink there (very expensive) but it's close to Notre Dame.
The walk along the Sienne at any point is highly recommended. But if you can, start at Point Neuf which is the oldest bridge in Paris.
She also recommends a boat trip - Bateaux Mouche.
Sacre Coeur (Sacred Heart) area is the most touristic area of Paris but the church is beautiful and it's on the biggest hill in Paris so the view is spectacular. (But don't eat there!).
Places to avoid (unless you want to see the Moulin Rouge and plenty of sex shops) is the whole area around the Place de clichy and Pagale.
Cheap Hotels/HostelsThere's plenty of cheaper hotels near the Opera Garnier which is very central
There's also some nice hotels around the Villiers
A friend has this bed and breakfast;
www.beehome.fr which is lovely, for the price of a three star hotel you'd get the equivalent of a suite but it may be a bit more expensive than you're looking for. (if you want more info, then you can send me a message on FB if you like)
Time your bookings well, a friend booked this hotel
http://www.hotel-bedford.com/ but didn't book direct and instead went on to all the price comparison sites and eventually got a fabulous deal at the last minute.
Sorry this is so long! She's very keen on her home town and now I want to go!!!!
Enjoy.