Most of the affordable and ethnic places are open on Mondays. It's primarily the chef-driven, upscale places that are closed that day of the week. And even in that group, many are open Mondays. These include MK, Naha, RPM Steak, Boka, Shanghai Terrace, Blackbird, NoMI Kitchen, Travelle, The Lobby, Brindille, and Spiaggia.
If you're not necessarily focused on upscale places, then the decision is just like any other night of the week. Some of my favorites include Dos Urban Cantina, Salero, La Sirena Clandestina, Lula Cafe, Piccolo Sogno, Dusek's, the Bristol, GT Fish, Perennial Virant, Mercat a la Planxa, Seven Lions, Quartino, Mixteco Grill, Yusho, Anteprima, La Sardine, Salpicon, tesori, Carnivale, and the Florentine.