Hi Creamfinger -- welcome to my world. Folks who don't have to monitor their sodium intake have no idea how much salt is automatically added to prepared foods -- in the supermarkets as well as restaurants. As a diabetic with multiple food limitations, salt is definitely one of them. With so much hypertension and heart disease in our nation, I am constantly (and sadly) aware of the lack of attention paid to this element in the food world. Instead of increasing the manufacturing of low-salt options in the marketplace, there has instead been a decrease. The reason is simple: salted food tastes good. Sales go down, and the manufacturer pulls the plug. Triscuit used to have a low sodium cracker buit no more. Trader Joe's had some salt free chips though all but one have been replaced by "low" instead of "no" salt. However, TJ's does sell various no/low sodium products.
As far as restaurants are concerned, any food that is NOT freshly prepared to order is usually on the "no" list. For instance, in Italian food, it's obvious that lasagna is out; however, any pasta dish made with a pre-cooked sauce is also a definite no-no as well as casseroles from any cuisine. Most Mexican food -- don't even ask. There are huge amounts of sodium hidden in cheese - including (would you believe), cottage cheese, soups (as you mentioned), chips, crackers, pickles, chilis, bread, salted butter, popcorn, condiments and sauces of almost every kind. Prepared tuna salad is usually loaded. Although low-sodium soy sauces are available in Asian restaurants, even those pack a whalloping amount of sodium. Gelson's sells a prepared no-salt chicken.
With few exceptions, I don't really know of any "designated" places that cater to us. It's all about checking with the restaurant beforehand to find out so that you're not disappointed at the table. Can they prepare your steak, poultry or fish without salt? Is there salt in your hamburger meat? Is there salt in your scrambled eggs? Can the soy sauce be omited from the stir-fry? Servorg's suggestion of Follow-Your-Heart is a good one because the wait staff is very knowledgeable about the menu ingredients, and they aim to please. There is a good Chinese restaurant at Ventura and Topanga called Super Wok that prides itself on preparing healthy foods. I'm pretty sure that a request for no salt or soy sauce would be honored. Deli's are good if their roast beef or turkey is unsalted.
The condiment thing is so difficult. Especially if you're a foodie. Sure, we can have the baked potato with sour cream and chives -- but is there salt in the butter? Have you ever had a potato without salt? Yuk. Morton makes a product called "Lite Salt" which is 1/2 salt and 1/2 salt substitute. You may want to carry some with you. Heinz makes a salt free ketchup. Ordering a salad is great if you don't mind eating it nekid -- unless you bring along your own dressing.
I don't mean to be a "bummer" about this -- I know you only asked for restaurant suggestions -- but until you've been doing this kind of diet for awhile, it's hard to realize how much salt is hidden in restaurant food. Start with places and foods that you already like and try to find out about the sodium content in their foods. Check the sodium content on every food product you buy -- including spices. Your limit of 2,000 mg can be achieved -- but not without search and discovery. Sadly, there is no easy answer or "place" to go. I rarely eat out anymore. It would be great if another chowhound can suggest restaurants for us. Take care of you. Good luck!