other than the fact that i'm from newport (plenty reason enough to go) you won't be able to get johnny cakes or stuffed quahogs (pronounced koe-hawgs) in mystic.
unfortunately, it's been a good 5 years since i've been able to get back, so it's anyone's guess which restaurants are still in business. christie's and salas's are sure to still be around;good family style dining downtown on the waterfront. clarkes cookhouse is also on the waterfront; the food is ok, but the place is mainly memorable for me due an amusing incident involving my best friend who was waitering (bussing?) and moi showing up after my very first encounter with a large bottle of cheap wine.
two places i used to chef at were the oceancliff hotel and the castle hill inn; thethe quality of the oceancliff's fare has gone up and down over the years due to ownership changes and the head chefs that come and go, but it does have nice views, especially around sunset. if you cand afford the inn at castle hill, you won't be dissappointed. as i recall, it's also just about right next to jaqueline kennedy's childhood home.
the white horse tavern has been going since the 1600's i think, so if you want authentic colonial atmosphere it's nice. it has a ghost, which my mom has seen. us kids used to do dishes there when my mom couldn't find or afford a baby-sitter. i never saw the ghost, but old mr. clark, the alcoholic head chef, was close enough.
there are still a couple of old-style diners which are good for breakfast and lunch; one near the bowling alley and the other off of the rotary near the entrance for the newport bridge. i think that this is the diner where you can still get johnny cakes for breakfast, with a side order of chorizo if you feel like it.
if you happen to be leaving the island via the bristol bridge around evening, it's worth stopping at balzano's for family style spaghetti and steamers.
hope you have the best of trips. feel free to pick up some johnnycake meal to send me.