Plenty of reasonable hotels in the $30-50 per night range.
Unless your friend is going to show you around a lot, a week is about the longest I'd stay in any single city in Vietnam. I've done SGN for that a couple of times in the last decade. I'm doing DAD next year for a week.
To join all the others, I wouldn't connect in Mainland China. HKG, TPE, NRT, SIN are all fine connection cities.