Hanoi:
Tons of hotels that can be recommended, from 1 - 4star, best bet is figuring out what area you want to be in and go from there. Would suggest something near Hoan Kiem Lake, Truc Bach Lake, Back Packers Area or West Lake. If you want 5 star then would suggest Sofitel Metropole or Intercontinental.
In Nha Trang there are two decent options for hotels that could be around 60USD - 80USD a night. 5 Star by Vietnam standards but located directly across the beach in good areas.
Muong Thanh Hotel
M??ng Thanh Nha Trang
Havana Best Western Hotel
There are a ton of hotels from 1 - 3 stars located throughout Nha Trang that can be found on Agoda/Trip Advisor if your looking for something else.
HCMC: There is a chain of hotels called A&EM.
ezHotel.vn: ??t pḥng khách s?n They are little boutique 2/3 star hotels but located throughout District 1 in key areas. For 5 star would suggest Park Hyatt or Intercon. If A&EM doesnt seem a good fit then check around a bit as lots of 3/4 stars that are good too.