Not all the top restaurants are closed on Sundays. Did you try Alinea? Yes, they might be booked, but you won't know for sure unless you try calling. Two other top chef type places open Sundays are NoMi and Spiaggia; both are excellent and eminently suitable for such an occasion.
Taking a slight step down from the rarefied air of the very top tables in town, I think North Pond is an excellent place for a romantic dinner, between the food, and the decor, and the exquisite setting in Lincoln Park. A second recommendation is Custom House, which is a short walk from the Palmer House.
Most of the well-known steakhouses and seafood restaurants are open Sundays as well, but I think of them as being a bit too noisy and boisterous for a romantic dinner. Similarly, there are lots more places open Sundays, including Sweets and Savories, Sola, MK, Cuatro, Meritage, Le Colonial, Vermilion, and others, but I think the above recommendations are more appropriate for your anniversary.