Fine dining near Paris Opera House

www.viamichelin.com gives you access to their restaurant listings, searchable by stars or by map. You might also enjoy reading some "top 10s" from the Guardian Travel Section.

Assume you are talking about the Opera Bastille. Take a look at the Michelin Guide. How about the 3-star L'Ambroisie on Place des Vosges. 500 euro might get you by.
Seriously though, the Michelin Guide has listings for (relatively) good value dining with short "inspectors" report. Bofinger jumps out as a classic brasserie just off the circle, but look around. We usually don't dine in the area but at our favorites in other parts of town.

If it were me, I'd look to try Chez Denise, or perhaps Verjus. Never been to either one, but they look very interesting to me.

Actually we're looking for a restaurant near the National Opera House, Opera Garnier. Thanks for your help.

Ah yes, so there does appear to be a dearth of fine dining nearby, eh? In the opposite direction and at about the same distance are Taillevent and Le Cinq. Either of these, along with a taxi to/from would be quite wonderful. Have you found anything suitable that's closer? It may become difficult soon to make reservations due to restaurant 'closed for holiday' times.

There is a pretty nice restaurant right in the Opera Garnier.
http://www.opera-restaurant.fr/en/photos