I haven't stayed at Milestay but thought I'd mention a good experience at the Adagio Bercy Village in January/February of this year. (It seems like ages ago, with all that's happened since!)
You mention that you like walking along the Seine. Though Bercy is not a place tourists typically think of for a walk along the Seine, climb the steps from the Parc de Bercy and you'll be treated to a wide pedestrian path along that side of the Seine, as well as a pedestrian-only bridge to the opposite bank. It's a modern-architecture paradise, with the Bibliothèque Nationale, the Josephine Baker swimming pool, and other interesting structures.
The Cour Saint-Émilion has a mini Carrefour, a Nicolas, and adequate restaurants if you don't want to fix lunch or dinner in the kitchenette that day but don't want to travel far, either.
Métro access is efficient. Line 14, automated and thus minimally affected during strikes, gives fast access to the Rive Droite. For other destinations, the transfer to Line 6 at Bercy is handy, and a walking transfer from the Gare de Lyon to Line 10 at Austerlitz is more interesting, and not much slower, than the endless underground passageways of Châtelet–Les Halles.
With any "apart'hotel", if you'll be staying a week or more, it doesn't hurt to contact the hotel directly to inquire about weekly rates. Though I almost always recommend booking through a hotel chain's Web site, this is one case where a central booking engine might not know about all of the available rates. (I would avoid third-party booking sites, especially now, given the many disagreements reported here between guests, Web site operators and hotels, over changes and refunds.)
