For a couple of years I lived out of suitcases, my "home base" was in Chicago, so I stayed in hotels all over. Had great success with Priceline bidding (use biddingfortravel to guess what hotel you are going to get), but understand if that isn't for you.
I don't think I've stayed at the Hampton Downtown North, but based on the map it's in a great area. ETA: Technically this hotel is in the loop (rather than River North) and you'll need to walk across the river to get to the main shopping portions of Michigan, but it's an easy walk.
I rarely paid more than $100 a night, but if downtown was expensive, I would stay out by O'Hare and take the blue line back and forth, which isn't ideal for a nice mother-daughter weekend. I'd look into the Inn of Chicago and the Tremont. Both of these hotels are older with small rooms and tend to be cheaper, but they were clean (at least three years ago) and in great locations.