Well, the best PLACE to eat in Anna is at my house.

I'm not sure I can get onboard with a "Best" Restaurant in Anna, though.
Italian Villa has great NYC style pizza exactly like I had on the East Coast - the kind you fold over on itself to eat. They sell it by the slice too - which is unheard of here, but the norm there. I also like that they have Kendall Jackson Chardonnay.
I don't have anything good to say about
My Estrella and their flour tortillas are no better than the ones you buy at Sam's Club.
Jury is still out on
Crow's Cafe. I'm not sure if we will ever go back to see if things improved.
Both donut places are REALLY good.
Since you are new to the area my suggestion would be
Jalepeno Tree in McKinney as the best near Anna restaurant. They have fresh handmade flour and corn tortillas and their chicken flautas are AWESOME. My kids love going there because they chow on the tortillas and they have free soft serve ice cream. We probably go there at least once a week. It also has a full bar if that interests you.