Udon in Little Tokyo?
Suehiro Cafe is a few doors down from the museum and serves up a good bowl of udon as one of the featured items on its huge menu (some things are good, some are so-so). Open long hours, and a nice bookshelf full of manga to read/puzzle over while you slurp.
Re Mitsuwa, it's been recently reported that the mall has been sold and is to be converted into a Korean-oriented mall to service the many Korean-American residents who've been moving into downtown. It will be missed. (Personally, I don't think that mall has been the same since the movie theaters closed on the top floor--my age is showing, again.)
337 E 1st St, Los Angeles, CA 90012
333 S Alameda St # 100, Los Angeles, CA
Hold on! I study martial arts at a dojo in Yaohan Plaza 3 times a week. And I know for a fact that the mall has not changed AT ALL so far. It has simply changed hands on paper. AND there is no definite concensus on the future of that property. The Korean-Am. theme is simply being explored, as one of many possible options.
For now, Honda-Ya, Sushi Go 55, Mitsuwa Supermarket, Beard Papa's, and many other Japanese businesses are still fully up and running at Yaohan Plaza...
... Which leads me to my vote for the Nabeyaki Udon at Honda-Ya. Your friend will enjoy the decor and the food.
Lately I've been going to Sakura in the Mitsuwa Market at Alameda & 4th St. and JANM is at Alameda & 1st St.(3 block walk). Order your food at the cashier and they call your number when its ready kind of place. I get the beef udon most of the time and its pretty good. Udon and ramen can be ordered small or large. They also have other items like chicken katsu curry and teriyaki bowls. Prices are very reasonable and the food is good. There's also a Beard Pappa's on the first floor.
You get one hour free unvalidated parking in the Mitsuwa parking structure and if you spend $10 you'll get 2 hours of free parking. Ask for your receipt from Sakura and give it to the parking lot cashier (2 people at Sakura will come to around $10-$15).
Sakura hours 9:30am-6:00pm
JANM- Free admission every 3rd Thursday of the month and free every Thursday from 5pm-8pm.