Having lived in SoHo's neighboring Lower East Side for over 5 years, I have spent many of my weekend evenings in the area, sampling the neighborhood fare. In addition, I know that suggesting restaurants can be a completely subjective matter.......
Regardless, I have outlined a few below that would definitely fit your criteria above.
Kittichai 60 Thompson St. 212-219-2000 Thai
Lure Fishbar 142 Mercer St. 212-431-7676 Seafood
Mercer Kitchen 99 Prince St. 212-966-5454 American (New), French
Balthazar 80 Spring St. 212-965-1414 French (Brasserie)
As always, you can always use the Zagat Survey link below to find more in depth descriptions of each.