Hoi An town itself is a little bit inland. The beach is some distance away - note that roads in Vietnam are always slow, don't judge distances by Western travel times. Also, the really big beaches are in Da Nang (where the airport and train station are, 40-60 minutes away). But Hoi An town is very much worth visiting.
Ha Long Bay is a must. I'd recommend an overnight cruise there. I did it in a day trip myself (using a "VIP bus" that took the faster highway without stopping), but regretted it. There's definitely a lot of tourist-trap crap in Ha Long Bay, but it's popular for a reason.
Can't speak to Da Lat or Phu Quoc, but you should consider Hue as well. A train trip between Da Nang and Hue is a good way to experience some of the best Vietnamese scenery without committing to the full long, slow Reunification Express journey.
The Ha Giang loop in the north is wonderful for a bike trip, but I guess you're going there for a relaxing holiday with your partner, so it is probably not applicable.
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