This seems like a tad too much moving around for my tastes, but if you like to keep on the go so be it. Re Hanoi. We went there last year and loved it. Go to the Opera House, if you're lucky they'll be some special show on while you're in town (we were lucky) also make sure you stay in the "Old Section" it's the most interesting. There are numerous tour agents for Halong Bay and tours at various prices. You have an option of sleeping on the boat or putting up in a hotel at Cat Ba Island. We opted for the boat and had a lovely cabin, however, we both felt that we should have stayed in the hotel and had a chance to walk around a bit and find a restaurant serving better food than the cheap stuff served on the boat.
Many people told us a trip to Sapa is worthwhile, so you may consider there from Hanoi rather than going all the way to Hoi An.