In my opinion, the recommended rest cycles in 5E D&D are much better that the times that were laid out in the fourth edition rules, though I find myself liking some of the older school rest ideas. I know their are those that want to think of their characters more as "Superheroes" where they can be nearly totally spent on spells, special abilities and out of hit-points and after a nights rest they are all back up to full and ready to go (this was sort of the 4E model).
I typically like a slower paced recovery, where the party must make hard choices of whether to push on or try to rest up. In this regard I think 5E does a decent job out of the box of splitting the difference between the ultra fast model of 4E and the very slow old school model of recovery (1hp + Level + Con modifier, was the one I used to use). I do think some modification can be made to the 5E rest model (see entry Wounds in D&D 5th Edition if making recovery a little more difficult), but for the most part it stands as a viable model.
That said, there are definitely times where you want a session to be more fast paced, possibly with a tight time constraint, such that the story doesn't seem to allow even a short rest to be had. For these cases I created the following items and/or magical effects that can be found or encountered by the party in scenarios where the party might want to rest, but it is simply not a good location or the situation that they are in, makes actually taking a rest be problematic.
I'm currently thinking about a more energy based system for spells that is compatible with 5E, but without totally changing this or adding a spell level recovery system, the follow items grant a mechanism for players to sort of have an "Ace in the Hole", where they can regain spells much more quickly.
If you use the potion side-effect table, where consuming multiple potions in too short of a time must be rolled for on a table, possibly causing deadly side effects, may be enough of a deterrent stock piling a large store of these potions and then being able to replenish all of a characters spells and daily powers multiple times over in the course of short adventure. Using this side-effect however may prevent the benefits of implementing this system in the first place.
Mana Draught: the least powerful of the mana potions, this allows one 1 spell level to be regained. Thus after quaffing this potion a wizard could cast a first level spell, consuming multiple can allow multiple 1st level spells to be cast, but does not allow a 2nd level spell level to be gained.
Mana Potion: Like a Mana Draught, but this grants two spell levels back, either in the form of two 1st level spells or one 2nd level spell. To regain two 1st level spells the drinker simply consumes half of the potion, and then the other half. If they only desire one 1st level spell regained, they may choose to drink half of the potion as save the other half for another time.
Mana Elixir: This is similar to a Mana Potion, but it contains four spell levels, which can be regained in any of the following ways: 1x4th, 1x3rd+1x1st, 2x2nd, 1x2nd+2x1st, or 4x1st. Essentially this has 4 spell levels in it and can be consumed in quarters to regain any of the following combinations, even at separate times. So 1/4th could be drank to gain a 1st level spell, then at so other time the rest can be consumed to regain a 3rd level spell.
Potion of Vigor: Consuming one of these potions allow the drinker to regain a Hit Dice, these may be spent in the normal means, but do require a short rest after drinking the potion to actually recover hit points. Consuming a Potion of Vigor may not allow the drinker to exceed the maximum hit dice, determined by their level that they may have at one time.
Potion of Recovery: This grants most benefits of a short rest, thus powers that return after a short rest are regained, and hit dice may be spent provided the drinker of the potion has them to spend. When hit dice are spent using this potion, they may only spend a maximum of three.
Elixir of Recovery: This grants most benefits of a long rest, the only exception is casters do not regain any spell levels back for consuming this potion, all other abilities that return over a long rest are regained, as well as the recover hit dice as if a long rest was taken.
Enchanted Grove: Those is spells can feel something is special about this grove, and a feeling of peace can be felt upon entering the grove. When the party rests in this area they gain all the benefits of an Elixir of Recovery upon taking a short rest.
Way Point of Recovery: This is basically taking a page out of modern video games, where in locations where it is particularly dangerous to linger, travelers were required to forced-march through the territory until the advent of these arcane platforms. Travelers simply need the activation ingredients (or maybe there are ingredients on hand, or the Way Point simply recharges every few days).
Upon activation, all those that at within the area of the effect (typically 20 foot radius of monolith or all those on the platform) are recovered as if a Long Rest was taken. In very dangerous areas these my be located 20 to thirty miles apart, with the occasional way-point having been destroyed or may be non-functional.
When adventure scenarios are imagined sometimes they just don't "fit" into a particular game system's mechanics, so as a DM, you can either alter the scenario, which may or may not work...or you can alter the mechanics. This just briefly touches on some of the easy things that can be done to subtlety alter the game mechanics to allow your party to be "push through" even when it seems they are all tapped out.
As a player these items are very attractive, because knowing you can reactive a power once it is used, if the situations arise then it would allow me to be "less stingy" if I see a situation where that power seems like it could be used for a heroic action, as if an even better situation comes up or it's required that I have the same ability to overcome an obstacle, then no longer do I have to rest (possibly 8 hours), I can simply quaff a potion and reuse it. Sure, I'm out of the potion, but that's sort of the definition of where it's meant to be used.
As a DM, I like the idea of giving the players items such as this, especially in the Magical Fruit/Fountain variety, as those that don't take advantage of this simply lose the regain ability when the item expires, but those that do have the chance for especially heroic moments.