We did end up at a nice cafe, quite western-ish, looks like it's run by a christian organisation. This did solve an emerging lunch conundrum, which was great. Would definitely return.
After lunch we walked into the city and went to a camping store which sells these great water filters made by Katadyn. We had been looking for one, and they had them. After some 'discussion' (I use the word in the very loosest sense), we managed a purchase (it's always exciting when I can use a card instead of bundles of cash), and caught the trolley bus home.
So some small progress: a water filter and cleaner floors.
Here's a video of some driving in Mongolia.