Hoi An Vietnam is fundamentally a tourist town. In the tourist areas, your best bet for local food are the food stalls open for lunch in and near the morning market.
This was the last stop on our trip, and so we were low on adventurousness and enthusiasm. Hoping other chowhounds will be able to explore more:
Bale Well - This probably was started to cater to the Vietnamese tourist population, but is now overrun by western tourists. Do not let this stop you from trying it! Set meal of two different types of pork with all the fixings to make wraps, pancakes, and dessert. The pork was tasty and of good quality (liked the satay more than the other option) generous with the herbs. Greasy and tasty.
Banh Mi Phoung - Really outstanding Banh Mi. A lot of proteins to pick from, great ratio of herbs to vegetables to meat to spreads to bread. Proteins of good quality. We had ours with the added chili sauce. Would highly recommend.
Cao Lau night outdoor stand in front of the light blue historical building on the same side and block as the Mermaid restaurant. Solid. I liked that they gave more herbs and chilies than the western tourist restaurants but it wasn't super better than what you could get from Ms. Vy's numerous restaurants.
Cargo Club Cafe - we didn't go to the upstairs restaurant, but did spend a couple mornings at the cafe. The cafe is OK their croissants and pastries are of good quality by Western standards but not exemplary and somewhat pricey. Coffee is also fine. Nice location.
Cham Cham - small tourist oriented restaurant. Food was Ok. Flavors were good but meat was tough and rubbery. Liked the sweet and sour pork. Cheap beer!
Cocobox - cold pressed juices. OK. Very pricey and somewhat watery. Combinations, unfortunately, were mostly western centric, wish they used more local fruit/vegetables/herbs.
Highlands Coffee - Vietnamese equivalent of Peet's or Starbucks. Really enjoyed their hazelnut coffee freeze with jelly as a dessert. Clean bathrooms, a lot of space to lounge around, remains cool in hot weather, has reliable wifi.
Little Menu - Solid quiet restaurant. Food takes a bit longer than other places to come out. Flavors are nice and quality is good - it's a very solid option. Nothing really stood out as spectacular. I liked that there was an option to try all the Hoi An appetizer specialties on one platter.
Mango Mango - Vietnamese fusion restaurant. Reminded me highly of Roy's (the high end Hawaiian chain). The food was of good quality and flavorful but was somewhat generic in flavors used (mango salsa, mild use of tamarind etc.). Good cocktails.
The Market Restaurant - Ms. Vy's restaurant specializing in streetfood - was fine, but no better or worse than any others. A nice positive is you can walk around and watch the various cooks making the different street food specialities. You, however, sit at a table and order off the menu - it's not a food court.
Mermaid Restaurant - One of many of Ms. Vy's restaurants. This one was OK had a flavorful spicy seafood hot pot.
Morning Glory Restaurant (would make dinner reservations a day or two ahead) - Our favorite of Ms. Vy's restaurants. Very flavorful food with more attention to detail than the others. Really enjoyed the mung bean pancakes (prepared with more finesse, flavor and less grease than other places) and the prawn curry (subtly spicy but lots of nice savory, coconut and herbal flavors)
Reaching Out Teahouse - A silent teahouse started and run by the hearing/speaking impaired. Very relaxing environment and nice Vietnamese tea blends and service. Great place to read and enjoy a cup of tea.
Street Donuts - The one we tried was stale and used sub par oils/fats for frying.