I trust that you may come up with better ideas than I can, but for what it's worth, here's my concept:
LatinTutor.com, all caps (and please include the .COM part), but with the L and T just slightly larger than the other caps, done in the style of the NYC subway mosaics. I really like the look (and colors -- but be creative too) of the subwayMosaicNYC image, especially the rectangular borders immediately surrounding the words.
i'm CRAZY about the detail of the tiles in the tesseradetail image: the different shades of blue and green in the background, and the fact that the tiles in the letters are hand cut while the others are not, and the way the background tiles trace the outline of the letters. wow!
I like the subway mosaics because while the mosaic says "Roman" the subway mosaic says "New York" -- and I want the logo to hint "a Latin teacher who understands New York private schools." The goal would be inspiring confidence in wealthy NYC moms who want the best possible tutor for their kid, and are willing to pay a bit more.
I love the subway idea, but it needs to be executed really well, or it will look cheesy.
have a different idea? go for it! another idea i could be into would be LATINTUTOR.COM in camel case (L and T slightly bigger, but all CAPS) in a font like trajan, so it looks like it's carved in stone.