Originally Posted by
toomanybooks
So maybe that would work, switching every 4 days.
Probably not in this case.
Switching every 4 nights gets you 8 stays (7 × 4 nights + 1 × 2 night stay).
Getting gold would then require 10 nights which would put you at a minimum of 18 stays, or 2 short on stays unless on a challenge (i.e., you'd hit gold on nights before you could on stays). Of course if the OP is going for diamond rather than gold, it's different because then it's only 12 stays instead of 20 nights, which might be easier to achieve.
One thing I would suggest is that the OP wants to be on points + points or points + variable miles for this stay and not points + fixed miles, which work better for those with shorter stays.
Earning 2 miles/dollar on Virgin Atlantic would mean that they could earn 10k miles with $5k of spend - meaning that they would get an extra 20k points immediately if they average $166.67 per night (including incidentals). Alternatively they would get 20k extra points with $4,000 of spend if on points + points, but wouldn't be eligible for any airline bonus promotions in future unless they changed their preferences.
It might make sense to check out after 10 nights, do 4 nights in another Hilton hotel and then 16 more nights to make sure that the silver status hits immediately to earn bonus points (1.5 points/dollar) on the last 20 nights.