Long Rest = NARRATIVE Week
...that can be five days, seven days, ten days: it varies to suit a narrative week of downtime, and is imprecisely enumerated by design, so it can't be gamed with mechanical shenanigans like rest-casting...
...as for safe havens, i prefer coupling rest benefits to the fifth-edition lifestyle definitions...
WRETCHED - No rest benefits.
SQUALID - Staves Exhaustion only.
POOR - Short Rests only.
MODEST - Standard Long Rests (half hit-dice).
COMFORTABLE - Long Rests + all hit-dice.
WEALTHY - Half-duration Long Rests + all hit-dice.
ARISTROCRATIC - Wealthy Long Rest + Inspiration.
...short rests are similarly a NARRATIVE shift (anywhere from six to ten hours) but also interact with exhaustion subject to the same lifestyle constraints: i.e. a WRETCHED night's sleep requires an exhaustion check in the morning while a SQUALID short rest won't, but you need to short rest in POOR or better conditions to recover from a level of exhaustion...
...as for effect durations, i simply bump everything greater than one round up by one level...
1 MINUTE = 10 MINUTES
10 MINUTES = 1 HOUR
1 HOUR = 8 HOURS
8 HOURS = 1 DAY
1 DAY = 1 WEEK
1 WEEK = 1 MONTH
1 MONTH = 1 SEASON
...note that these duration adjustments do not apply to downtime activities, as the whole point of gritty realism is to foster more natural narrative pacing and downtime engagement is a big part of that...
...i'll also note that some DMs couple gritty realism with slow natural healing (i.e. use your hit dice to heal) but i suspect that may throw off game balance and won't advocate for it until i have personal experience that it works well...