The JW Marriott is a well designed hotel, and the restaurant has a good reputation - but it's miles from town. Probably 30 minutes in a taxi at a normal time of day, but I could imagine it taking closer to an hour in the evening rush.
The HGI is just on the edge of the French Quarter, and is in walking distance of the Old Quarter.
What you do on your morning before heading to the airport does depend on what day of the week it is. Many museums (including the mausoleum and the Temple of Literature) are shut on Mondays; a couple also on Fridays. I assume your tour will take you to the other Hanoi Hilton, the Temple of Literature and the Mausoleum complex, as well as around the Old Quarter, but if not then you could consider doing one or more of those. I've been rather lax on going to museums, but a friend had very good things to say about the Museum of Fine Arts, and the Women's Museum - the latter is quite close to the HGI.
Wandering the streets and drinking coffee is fun too, at least until you get fed up of the motorcycles or the heat (worth bearing in mind, it'll start getting hot soon).
Thank you everyone who has given advice so far. I don't have enough points for two nights at the Hilton, and it's a bit pricey per night, but I now am holding that reservation, too. I'll have to decide.
Also, specific thanks on mentioning the Monday closures. My second half day IS a Monday, so I'll try to do museums that won't be on my full day tour on Saturday and hang around drinking coffee on Monday. Several years ago, a friend was in Paris for one full day, took a cab to the Louvre only to discover it was closed for the day. A nice security guard let her and her sister in anyway, so they were able to practically have the place to themselves.