The Pioneer Saloon is an institution. It's old school, there's taxidermy on the walls and I don't even eat animals but I still love it (I get the trout or prawns). The bar is fun--we've struck up a lot of great conversations with people there. It can be very crowded with long waits but you are there during a quiet time. Everyone goes there--ranchers from the surrounding area, rich people that flew in on private jets, tourists.
Rickshaw is my favorite. If this is a solo trip for you, they have a little bar which is nice. Popular and small but they have a nice fire pit outside for waiting. Good wine.
Enoteca (Italian) is good. We usually eat at the bar. They are popular so we always call ahead (and are always told that all tables are reserved, but they can hold a couple of bar seats...). Nice wine selection, nice staff.
Christina's is wonderful. They only serve breakfast and lunch (and to-go meals), but they also have a bakery case with the best cookies. Christina is Italian and so it's not just the usual American stuff. I always go at least once for a big box of cookies.
The Kneadery is good for breakfast. It's in a historic log cabin. And I love love love Konditeri, out at the lodge, for breakfast/lunch/baked goods, but I bet that won't work for you as you'll be on the mountain during those meals and it's outside of town.
If you just wanted a sandwich or salad, I like Bigwood Bread and also, Atkinson's Grocery, which has a small but good, fresh salad bar in the produce section. Atkinson's is a great grocery for whatever you need.
Roundhouse (from 1937) is my favorite on the mountain. If you don't want to take the time to sit and be waited on at lunch during the ski day--I know not everyone does--at least make it a pit stop at some point. You can get a glass of water from the dispenser near the door and look at the old photos and the 4-sided fireplace. If you want something less expensive than everything else on the mountain, check out the Lookout. It's Mexican, and it's not the best Mexican you'll ever have, but it's pretty good, and reasonable prices, and the restroom is right by the doors--not down or up stairs. It's kind of an ugly building and not as nice as the newer lodges, so prices are lower to get people to go there. Seattle Lodge is very comfortable with a good fireplace, great views and slightly better than average lodge food. That's where most people like to eat lunch.
My biggest tip is that if you just need a quick restroom break when on Seattle Ridge, ski past the main entrance, down to doors that lead into a lower level where the restroom is. (Can you tell a big pet peeve of mine is having to walk up or down stairs in ski boots?). My second tip is that there are free cubbies to store your things in River Run Lodge, near the fireplace. That is where you'd naturally start your day if staying in Ketchum. Oh, and, ski storage at Pete Lane's, at the River Run base, tucked away in the corner, is only $5/night for people not staying at a SV property. So if you don't like carrying your skis consider doing that.