Depending on your definition of "near the strip" I'd consider the Wild Sage Cafe. It is in a little strip mall/office area on Warm Springs and Bermuda (southeast of the strip by about 5 blocks or so).

Ate there on my last trip on some one else's recommendation and thought it was excellent. With an entree price of ~$18-30 and appetizer in the $8-15 range, it fits in your price budget with some room for wine and desserts.

The ambiance is quiet, with a very nice decor. Food is American with flair. Below are some links. I thought it was well worth the short trip off the Strip.

http://lasvegas.citysearch.com/profile?id=11342052

http://www.aaamenus.com/wildsage.html