The Mercure Opera Garnier would be a perfect base. It is tucked away in a little street across from la gare St Lazare and is a 5 minutes walk to l Opera Garnier.
The Paris Renaissance Vendome was reasonably priced for the category when we stayed last week. Would second Earl's Latin Quarter suggestion. There is a great buzz about the place. Just walk out and you there.
www.Grandhotelleveque.com We have stayed here several times over the years and was a reccommendation from friends years ago. The hotel is not very luxurious, but very clean with air con. Its located on Rue Cler, a very local Parisien market street, within very easy walking distance to the Eiffel tower etc.. It books up very quicly so you need to be on the ball booking it in advance. Another one we have stayed in is Hotel Duquense, also located near here, nicer hotel, more expensive and not on as nice a street !